TY - UNPB
AU - Dmitrií A. Sadovskií
TI - Classical and quantum Hamiltonian monodromy
T2 - a case study of the hyperbolic circular billiard
Y1 - 2010/07/02/last-version
Y2 - 2008///initiated
N1 - work largely accomplished in 2008-2010, intended as a book
L1 - LaTeX/monodromy/scatter/tutorial.pdf
LA - English
ID - DS-tutorial
ER -
TY - UNPB
AU - Dmitrií A. Sadovskií
TI - On the geometry of resonant oscillator systems
Y1 - 2010/09//last-version
AB - We reduce the $S^1$-symmetry of resonant 2- and 3-oscillators and relate reduced systems obtained for different resonances. In particular, we map explicitly the reduced system of the $m_1{:}m_2$ oscillator (with $m_1$ and $m_2$ arbitrary positive integers) to that of the regular $1{:}1$ oscillator.
L1 - Maple/CPn/tex/resonances.tex
LA - English
ID - DS-resonances
ER -
TY - UNPB
TI - Reduced quantization near a hyperbolic singularity
AU - Fontanari,Daniele
AU - Sadovskií,Dmitrií A.
AB - We consider the energy spectra of simple quantum mechanical systems with nontrivial discrete isotropy group $G$, notably the planar pendulum and the Euler top, near the energy of the hyperbolic fibre (separatrix) of the correspnding classical Hamiltonian system and analyze the property of these spectra to become seemingly ``regular'' for each subfamily of quantum states transforming according to the same irreducible representation of $G$. Our explanation of this phenomenon involves a combination of the WKB quantization principle for integrable systems, reduction of discrete symmetries, and uniform semiclassical theories.
N2 - Initially started in 2008 on the example of the Euler top
L1 - LaTeX/Etop/Etop.tex
LA - English
ID - DS-Etop
ER -
TY - UNPB
TI - Coherent states for the quantum complete rigid rotor
AU - Fontanari,Daniele
AU - Sadovskií,Dmitrií A.
JF - European Physical Journal D
JO - Europ. Phys. J. D
J1 - EPJD
AB - Motivated by the possibility to describe orientations of quantum triaxial rigid rotors, such as molecules, with respect to both internal (body-fixed) and external (laboratory) frames, we go through the theory of coherent states and design the appropriate family of coherent states on T SO(3), the classical phase space of the freely rotating rigid body (the Euler top). We pay particular attention to the resolution of identity property in order to establish the explicit relation between the parameters of the coherent states and classical phase-space variables, actions and angles.
N2 - Submitted 20 December 2016
L1 - LaTeX/daniele/tso3/coherentTSO(3).pdf
LA - English
ID - DF-TsSO3cs
ER -
TY - JOUR
TI - Nikolaí N. Nekhoroshev
AU - Alekseí Vl. Borisov
AU - Alekseí V. Bolsinov
AU - Anatolí I. Nejshtadt
AU - Dmitrií A. Sadovskií
AU - Boris I. Zhilinskií
JF - Regular and Chaotic Dynamics
T2 - On the 70th Birthday of Nikolaí N. Nekhoroshev
JA - Reg. & Chao. Dyn.
J1 - RCD
VL - 21
IS - 6
SP - 593
EP - 598
PY - 2016/12//
LA - English
PB - Pleiades Publishing, Ltd.
SN - 1560-3547
U1 - 10.1134/S1560354716060010
ID - kolya-foreword-2016
UR - http://rcd.ics.org.ru/upload/iblock/366/RCD593.pdf
L1 - biblio/dima/foreword-RCD21-2016p593.pdf
L2 - LaTeX/kolya/foreword-2016.pdf
L3 - LaTeX/kolya/foreword-2016-ru.pdf
ER -
TY - JOUR
TI - Nekhoroshev's approach to Hamiltonian monodromy
AU - Dmitrií A. Sadovskií
JF - Regular and Chaotic Dynamics
JA - Reg. & Chao. Dyn.
J1 - RCD
T2 - memorial issue on the 70th Birthday of Nikolaí N. Nekhoroshev
ED - Alekseí Vl. Borisov
VL - 21
IS - 6
SP - 720
EP - 759
Y2 - 2016/11/10/accepted
PY - 2016/12/20/online
AB - Using the hyperbolic circular billiard, introduced in [31] by Delos et al. as possibly the simplest system with Hamiltonian monodromy, we illustrate the method developed by N. N. Nekhoroshev and coauthors [48] to uncover this phenomenon. Nekhoroshev's very original geometric approach reflects his profound insight into Hamiltonian monodromy as a general topological property of fibrations. We take advantage of the possibility of having closed form elementary function expressions for all quantities in our system in order to provide the most explicit and detailed explanation of Hamiltonian monodromy and its relation to similar phenomena in other domains.
N1 - an excerpt from the unfinished book project
KW - integrable fibration, Hamiltonian monodromy, first homology, A1 singularity
LA - English
PB - Pleiades Publishing, Ltd
SN - 1560-3547
U1 - 10.1134/S1560354716060101
U2 - 10.1134/S1560354716060113
L1 - biblio/dima/nnmethod-RCD720-2016.pdf
L2 - LaTeX/monodromy/scatter/nnmethod.pdf
ID - DS-nnmethod-2016
ER -
TY - JOUR
TI - Afterword to the paper by N. N. Nekhoroshev
AB - This afterword accompanies the last, previously unpublished work by N. N. Nekhoroshev (pp. 413--541 of this volume). In order to explain Nekhoroshev's motivations and objectives, we describe briefly the background of his involvement in the theory of Hamiltonian monodromy during the last years of his life and his role in the discovery of fractional monodromy which is the subject of this last paper. We tell the history of the manuscript. In order to further the understanding of Nekhoroshev's point of view include excerpts from Nekhoroshev's exchanges with the editors of ``Izvestia RAN''. We end with a brief biographic commentary which accompanies photographs and materials from the archive of N. N. Nekhoroshev. Together with the manuscript, they were kindly provided by Irina Vasil'eva, the late widow of N. N. Nekhoroshev. http://nd.ics.org.ru/nd1603008p/
AU - Dmitrií A. Sadovskií
JF - Nilenejnaya Dynamika
JO - Rus. J. Nonlin. Dyn.
VL - 12
IS - 3
SP - 543
EP - 553
U1 - 10.20537/nd1603008
UR - http://nd.ics.org.ru/upload/iblock/ef6/nd1603008p.pdf
L1 - biblio/dima/nd1603008p.pdf
L2 - LaTeX/kolya/afterword-drobobW1-2016.pdf
PY - 2016/10//
ID - DS-nnafterw-2016
LA - Russian
ER -
TY - JOUR
TI - Quantum manifestations of Nekhoroshev stability
AU - Daniele Fontanari
AU - Francesco Fassň
AU - Dmitrií A. Sadovskií
PY - 2016/07/19/
Y2 - 2016/07/22/online
JF - Physics Letters A
JO - Phys. Lett. A
J1 - PLA
VL - 380
SP - 3167
EP - 3172
PB - Elsevier
AB - We uncover quantum manifestations of classical Nekhoroshev theory of resonant dynamics using a simple quantum system of two coupled angular momenta with conserved equal magnitudes which corresponds to a perturbed classical integrable anisochronous Hamiltonian system.
KW - anisochronous system, coupled angular momenta, Nekhoroshev theorem, joint expectation value spectrum, resonant normal form, exponentially long time stability
LA - English
U1 - 10.1016/j.physleta.2016.07.047
ID - DF-lettS2xS2-PhLA2016
UR - http://authors.elsevier.com/a/1TWQv1LUy9Bfj0
ER -
TY - JOUR
TI - An application of Nekhoroshev theory to the study of the perturbed hydrogen atom
AU - Francesco Fassň
AU - Daniele Fontanari
AU - Dmitrií A. Sadovskií
PY - 2015/10/31/
JF - Mathematical Physics, Analysis and Geometry
JO - Math. Phys. Anal. Geom.
VL - 18
IS - 1
SP - 1
EP - 23
C7 - 30
PB - Springer Netherlands
SN - 1385-0172
AB - We return to the Keplerian or n-shell approximation to the hydrogen atom in the presence of weak static electric and magnetic fields. At the classical level, this is a Hamiltonian system with the phase space S2xS2. Its principal order Hamiltonian H_0 was known already to Pauli in 1926. H 0 defines an isochronous system with a linear flow on S 2 x S 2 and with frequencies depending on the external fields. Small perturbations of H 0 due to higher order terms can be studied by further normalization, either resonant or nonresonant. We study the question, raised previously, of how to decide for given parameters of the fields what normalization should be used and with regard to which resonances. We base this analysis on the Nekhoroshev theory--a branch of the Hamiltonian perturbation theory that complements the Kolmogorov-Arnold-Moser theorem. Our answer depends on the a priori choice of the maximal order N of resonances that are going to be taken into account (a cutoff). For any given N, there is a decomposition of the parameter space into resonant and nonresonant zones, and a normal form with a remainder of order \(\exp (-N)\) may be consistently constructed in each of such zones
KW - Perturbed hydrogen atom, n-shell, Resonances, Normal form, Nekhoroshev theory
KW - 37J40, 70H08, 70F05, 81V45, 37J40
LA - English
U1 - 10.1007/s11040-015-9200-y
ID - Fasso-hatomNekh-2015
UR - http://dx.doi.org/10.1007/s11040-015-9200-y
ER -
TY - JOUR
TI - Theoretical spectroscopic characterization at low temperatures of dimethyl sulfoxide: the role of anharmonicity
T2 - Spectroscopy and Dynamics of Medium-Sized Molecules and Clusters: Theory, Experiment, and Applications
AU - M. L. Senent
AU - S. Dalbouha
AU - A. Cuisset
AU - D. A. Sadovskii
JO - J. Phys. Chem. A
JF - The Journal of Physical Chemistry A
J1 - JPCA
VL - 119
IS - 37
SP - 9644
EP - 9652
PY - 2015/08/27/virtual special issue
U1 - 10.1021/acs.jpca.5b06941
ID - Senent-DMSOabinitio-JPC2015
N1 - Published as part of a virtual special issue
ER -
TY - JOUR
TI - Perturbations of the hydrogen atom by inhomogeneous static electric and magnetic fields
AU - Fontanari,Daniele
AU - Sadovskií,D.A.
JF - Journal of Physics A: Mathematical and Theoretical
JO - J. Phys. A: Math. Theor.
J1 - JoPA
VL - 48
IS - 9
SP - 095203
AB - The hydrogen atom is a specific, and physically relevant, Keplerian two-body system with one of the bodies assumed infinitely heavy. Isochronous integrable n-shell approximations for the perturbations of the hydrogen atom, known as Stark and Zeeman effects in the presence of homogeneous electric and magnetic fields, respectively, have been widely studied. In order to go beyond the set of linear systems, we considered perturbations by inhomogeneous electromagnetic fields. In particular, we found that the perturbation by a generic inhomogeneous magnetic field results in an approximately integrable anisochronous system which can be described as two rigid Euler tops coupled through higher order terms.
N2 - Received 23 July 2014, accepted for publication 13 January 2015
UR - http://stacks.iop.org/1751-8121/48/095203
U1 - 10.1088/1751-8113/48/9/095203
PY - 2015/03/06/
Y2 - 2015/02/04/
PB - IOP Publishing Ltd
ER -
TY - CHAP
TI - The sign exchange bifurcation in a family of linear Hamiltonian systems
AU - Cushman,R.
AU - Robbins,J.M.
AU - Sadovskií,D.A.
BT - Nonlinear physical systems: spectral analysis, stability, and bifurcations
A2 - Kirillov,O.N.
A2 - Pelinovsky,D.E.
SP - 41
EP - 65
PY - 2013/12/20/
U1 - 10.1002/9781118577608,
PB - Wiley
CY - New York
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/RHC-signexchange-nps2013-pp41-65-106.pdf
L1 - /home/dima/archive/biblio/dima/RHC-signexchange-nps2013-pp41-65-106.pdf
ER -
TY - JOUR
TI - Rotational structure of the five lowest frequency fundamental vibrational states of dimethylsulfoxide
AU - Cuisset,Arnaud
AU - Drumel,Marie-Aline Martin
AU - Hindle,Francis
AU - Mouret,Gaël
AU - Sadovskií,Dmitrií A.
JF - Chemical Physics Letters
JO - Chem. Phys. Lett.
J1 - CPL
VL - 586
IS - Suppl. C
SP - 10
EP - 15
PY - 2013/09/04/
PB - Elsevier
U1 - 10.1016/j.cplett.2013.09.029
SN - 0009-2614
UR - http://www.sciencedirect.com/science/article/pii/S0009261413011846
AB - We report on the successful extended analysis of the high-frequency (200-700GHz) part of the gas phase (sub)mm-wave spectra of dimethylsulfoxide (DMSO). The spectrum was recorded at 100kHz resolution using a solid state subTHz spectrometer. The five lowest energy fundamental vibrational states of DMSO with frequencies below 400cm-1 were observed as sidebands along with the main 0<-0 band. Neglecting the internal rotation of methyls, our rotational Hamiltonian reproduced the spectrum to the subMHz accuracy. We have found that the asymmetric bending state nu23 is the only low frequency fundamental vibrational state with the <> rotational structure uncovered in Cuisset et al. [1]. dmsomw 2013-09-04 15:03 (c) 2013 Elsevier
RP - IN FILE
ID - Cuisset-DMSOmw-2013
L1 - preprints/DMSOmw.pdf
ER -
TY - JOUR
TI - Gyroscopic destabilisation in polyatomic molecules. Rotational structure of the low-frequency bending vibrational states {$\nu_{23}$} and {$\nu_{11}$} of dimethylsulfoxyde ({DMSO})
AU - Cuisset,Arnaud
AU - Sadovskií,D.A.
JO - J. Chem. Phys.
JF - Journal of Chemical Physics
J1 - JCP
VL - 138
SP - 234302/1
EP - 18
PY - 2013/06/01/
U1 - 10.1063/1.4809738
RP - IN FILE
ID - Cuisset-DMSOnu23-JCP
L1 - preprints/DMSOnu23.pdf
ER -
TY - JOUR
TI - Gyroscopic destabilization of molecular rotation and quantum bifurcation observed in the structure of the {$\nu_{23}$} fundamental of dimethylsulfoxyde
AU - Cuisset,Arnaud
AU - Pirali,Olivier
AU - Sadovskií,D.A.
JO - Phys. Rev. Lett.
JF - Physical Review Letters
J1 - PRL
VL - 109
IS - 9
SP - 094101/1
EP - 4
PY - 2012/08/01/
PB - American Physical Society
U1 - 10.1103/PhysRevLett.109.094101
RP - IN FILE
UR - http://link.aps.org/doi/10.1103/PhysRevLett.109.094101
L1 - preprints/DMSOnu23lett.pdf
ID - Cuisset-DMSOnu23-letter
ER -
TY - JOUR
TI - Normalization and global analysis of perturbations of the hydrogen atom
AU - Efstathiou,K.
AU - Sadovskií,D.A.
VL - 82
IS - 3
JF - Reviews of Modern Physics
JA - Rev.Mod.Phys.
J1 - RMP
SP - 2099
EP - 2154
PY - 2010/08/03/
AB - The hydrogen atom perturbed by sufficiently small homogeneous static electric and magnetic fields of arbitrary mutual alignment is a specific perturbation of the Kepler system with three degrees of freedom and three parameters. Normalization of the Keplerian symmetry reveals that the parameter space is stratified into resonant zones of systems, each zone with an internal dynamical stratification of its own (Efstathiou, Sadovskií, and Zhilinskií, 2007, Proc. R. Soc. London, Ser. A 463, 1771). Based on the fully integrable approximation, the bundle of invariant tori of individual systems within zones is characterized globally and the qualitative dynamical stratification is uncovered. The techniques involved in this analysis are illustrated with the example of the 1:1 resonance zone (near orthogonal fields) whose structure is known at present. Applications in the corresponding quantum system are also described.
PB - American Physical Society
U1 - 10.1103/RevModPhys.82.2099
U2 - Copyright (C) 2011 The American Physical Society, prola@aps.org
RP - IN FILE
UR - http://link.aps.org/doi/10.1103/RevModPhys.82.2099
ID - KEDS-hatom-RMP2010
ER -
TY - JOUR
TI - Direct absorption transitions to highly excited polyads 8, 10, and 12 of methane
AU - Sadovskií,D.A.
AU - Kozlov,D.N.
AU - Radi,P.P.
JF - Physical Review A
JO - Phys.Rev.A
J1 - PRA
VL - 82
IS - 1
SP - 012503/1
EP - 17
PY - 2010/07/06/
PB - American Physical Society
U1 - 10.1103/PhysRevA.82.012503
ID - DAS-CH4polyads-PRA2010
RP - IN FILE
UR - http://link.aps.org/doi/10.1103/PhysRevA.82.012503
L1 - preprints/CH4P10P12.pdf
ER -
TY - JOUR
TI - Far-infrared high resolution synchrotron FTIR spectroscopy of the $\nu_{11}$ bending vibrational fundamental transition of dimethylsulfoxyde
AU - Cuisset,Arnaud
AU - Nanobashvili,Lia
AU - Smirnova,Irina
AU - Bocquet,Robin
AU - Hindle,Francis
AU - Mouret,Gaël
AU - Pirali,Olivier
AU - Roy,Pascale
AU - Sadovskií,D.A.
JO - Chem.Phys.Lett.
J1 - CPLett
VL - 492
IS - 1-3
SP - 30
EP - 34
PY - 2010/05/26/
U1 - 10.1016/j.cplett.2010.04.042
ID - Cuisset-DMSOnu11-CPL2010
RP - IN FILE
L1 - /home/dima/archive/biblio/dima/Cuisset-DMSO-CPL492-2010p30.pdf
UR - preprints/DMSOnu11.pdf
ER -
TY - JOUR
TI - Complete classification of qualitatively different perturbations of the hydrogen atom in weak near orthogonal electric and magnetic fields
AU - Efstathiou,K.
AU - Lukina,O.V.
AU - Sadovskií,D.A.
JO - J.Phys.A: Math.Theor.
JF - Journal of Physics A: Math. Theor.
J1 - JoPA
VL - 42
IS - 5
SP - 055209/1
EP - 29
PY - 2009///
U1 - 10.1088/1751-8113/42/5/055209
ID - Efstathiou-1:1-JPhA2009
ER -
TY - JOUR
T1 - Dynamical manifestations of Hamiltonian monodromy
AU - Delos,J.B.
AU - Dhont,G.
AU - Sadovskií,D.A.
AU - Zhilinskií,B.I.
JO - Ann. Phys.
JF - Annals of Physics
VL - 324
IS - 9
SP - 1953
EP - 1982
PY - 2009/09//
AB - Monodromy is the simplest obstruction to the existence of global action-angle variables in integrable Hamiltonian dynamical systems. We consider one of the simplest possible systems with monodromy: a particle in a circular box containing a cylindrically symmetric potential-energy barrier. Systems with monodromy have nontrivial smooth connections between their regular Liouville tori. We consider a dynamical connection produced by an appropriate time-dependent perturbation of our system. This turns studying monodromy into studying a physical process. We explain what aspects of this process are to be looked upon in order to uncover the interesting and somewhat unexpected dynamical behavior resulting from the nontrivial properties of the connection. We compute and analyze this behavior.
SN - 0003-4916
KW - Hamiltonian monodromy
KW - Energy-momentum map
UR - http://www.sciencedirect.com/science/article/B6WB1-4VXB8Y2-4/2/3b16857078ab21b8c6505456a7cfe8c8
U1 - 10.1016/j.aop.2009.03.008
ID - DelosAPhy2009-dynmon
ER -
TY - JOUR
TI - Most Typical 1:2 Resonant Perturbation of the Hydrogen Atom by Weak Electric and Magnetic Fields
AU - Efstathiou,K.
AU - Lukina,O.V.
AU - Sadovskii,D.A.
PB - APS
PY - 2008/12/19/
JO - Phys.Rev.Lett.
JF - Physical Review Letters
JA - Phys. Rev. Lett.
J1 - PRL
VL - 101
IS - 25
SP - 253003/1
EP - 4
ID - EfstathiouPRL2008-typ12
UR - http://link.aps.org/abstract/PRL/v101/e253003
U1 - 10.1103/PhysRevLett.101.253003
ER -
TY - JOUR
TI - Dynamical manifestations of Hamiltonian monodromy
AU - Delos,John B.
AU - Dhont,G.
AU - Sadovskií,D.A.
AU - Zhilinskií,B.I.
JO - Europhys.Lett.
VL - 83
SP - 24003/1
EP - 6
PY - 2008/07/04/
ID - Delos2008-pearl
U1 - 10/1209/0295-5075/83/24003
UR - http://purple.univ-littoral.fr/~dima/preprints/pearl-EPL83-2008-24003.pdf
ER -
TY - JOUR
TI - Classification of perturbations of the hydrogen atom by small static electric and magnetic fields
AU - Efstathiou,K.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Proceedings of the Royal Society of London, Series A Mathematical, Physical and Engineering Sciences
JO - Proc.Roy.Soc.A
VL - 463
IS - 2083
PY - 2007/07/08/
SP - 1771
EP - 1790
AB - We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields of all possible mutual orientations. Normalizing with regard to the Keplerian symmetry, we uncover resonances and conjecture that the parameter space of this family of dynamical systems is stratified into zones centred on the resonances. The 1:1 resonance corresponds to the orthogonal field limit, studied earlier by Cushman & Sadovskií 2000 (Physica 142, 166-196). We describe the structure of the 1:1 zone, where the system may have monodromy of different kinds, and consider briefly the 1:2 zone.
N1 - online 2007/05/15 (http://www.pubs.royalsoc.ac.uk/proceedingsa); received 2007/01/17, accepted 2007/03/13; ms.07PA0028
U1 - 10.1098/rspa.2007.1843
KW - perturbed Kepler system
KW - singular reduction
KW - energy-momentum map
KW - monodromy
ID - Efstathiou2007DS-zones-letter
UR - http://www.journals.royalsoc.ac.uk/content/g44318v573v04571
RP - IN FILE
L1 - /home/dima/public_html/preprints/RSPA20071843-eprint-20070515.pdf
L2 - http://purple.univ-littoral.fr/~dima/preprints/zones.pdf
ER -
TY - JOUR
TI - Local modes of silane within the framework of stretching vibrational polyads
AU - Crogman,H.
AU - Boudon,V.
AU - Sadovskii,D.A.
JF - European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics
JO - Europ.Phys.J.D
VL - 42
IS - 1
SP - 61
EP - 72
PY - 2007///
AB - We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes $\nu_1$ and $\nu_3$ of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad.
N2 - Received 9 Oct 2006 ms. D06412/ Received in final form 12 Dec 2006 / Published online (http://www.edpsciences.org/epjd) on Jan 19, 2007
PB - EDP Sciences, Societŕ Italiana di Fisica, Springer-Verlag
U1 - 10.1140/epjd/e2007-00011-3
M1 - 33.15.Mt, 33.20.Vq
KW - relative equilibrium
KW - vibrational polyad
KW - local mode
KW - complex projective space
ID - Crogman2007DS-LMRESi
UR - http://purple.univ-littoral.fr/~dima/preprints/silanelm.pdf
RP - IN FILE
L1 - /home/dima/public_html/preprints/silanelm.txt
ER -
TY - JOUR
TI - Hamiltonian systems with detuned $1{:}1{:}2$ resonance: Manifestation of bidromy
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Annals of Physics
JO - Ann.Phys.
VL - 322
IS - 1
PY - 2007/01//January Special Issue: 80 Years of Quantum Mechanics
A2 - Wilczek,Frank
SP - 164
EP - 200
PB - Academic Press
U1 - 10.1016/j.aop.2006.09.011
AB - We consider a generalization of the 1:1:2 resonant swing-spring [see H. Dullin, A. Giacobbe, R.H. Cushman, Physica D 190 (2004) 15] which is suggested both by the symmetries of this system and by its physical and in particular molecular realizations [see R.H. Cushman, H.R. Dullin, A. Giacobbe, D.D. Holm, M. Joyeux, P. Lynch, D.A. Sadovskii, B.I. Zhilinskii, Phys. Rev. Lett. 93 (2004) 024302-1-024302-4]. Our generic integrable system is detuned off the exact Fermi resonance 1:2. The three-dimensional (3D) image of its energy-momentum map EM consists either of two or three qualitatively different non-intersecting 3D regions: a regular region at low vibrational excitation, a region with monodromy similar to that studied for the exact resonance, and in some cases-an intermediate region in which the 3D set of regular values of EM is partially self-overlapping while remaining connected. In the presence of this latter region, the system has an interesting property which we called bidromy. We analyze monodromy and bidromy for a concrete integrable classical Hamiltonian system of three coupled oscillators and for its quantum analog. We also show that the bifurcation involved in the transition from the regular region to the region with monodromy can be regarded as a special resonant equivariant analog of the Hamiltonian Hopf bifurcation. [All rights reserved Elsevier]
KW - Fermi resonance
KW - energy-momentum map
KW - monodromy
KW - lattice defect theory
KW - Nonlinear dynamical systems and bifurcations
KW - Vibrational analysis molecular spectra
ID - Zhilinskii2007DS-HHopf-112
RP - IN FILE
L1 - /home/dima/public_html/preprints/bidromy-AnnPhys-322-2007p164.pdf
ER -
TY - JOUR
TI - Fractional monodromy of the $1{:}(-2)$ resonance
AU - Efstathiou,K.
AU - Cushman,R.H.
AU - Sadovskii,D.A.
JF - Advances in Mathematics
JO - Adv.Math.
VL - 209
IS - 1
SP - 241
EP - 273
PY - 2007/02/15/
AB - We give an analytic proof of the fractional monodromy theorem for the 1:-2 oscillator system with S^1 symmetry formulated by N.N. Nekhoroshev, D.A. Sadovskií, and B.I. Zhilinskií in C. R. Acad. Sci. Paris, Ser. I 335 (2002) 985\u2013988. Our proof is based on an analytic description of the Hamiltonian flow on the fibers of the integral map of this system.
N2 - received 19 Oct 2004 (AIM-244); accepted 9 May 2006; online 2006/07/12. Communicated by Tomasz S. Mrowka
KW - Liouville integrable system
KW - Singular toric fibration
KW - Monodromy
PB - Academic Press (Elsevier)
SN - 0001-8708
U1 - 10.1016/j.aim.2006.05.006
ID - Efstathiou2007DS-fracmono-konst
ER -
TY - JOUR
TI - Quantum monodromy and its generalizations and molecular manifestations
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Molecular Physics
JO - Mol.Phys.
VL - 104
IS - 16-17
PY - 2006/08/20/
SP - 2595
EP - 615
PB - Taylor & Francis
U1 - 10.1080/00268970600673363
AB - Quantum monodromy is a non-trivial qualitative characteristic of certain non-regular lattices formed by the joint eigenvalue spectrum of mutually commuting operators. The latter are typically the Hamiltonian (energy) and the momentum operator(s) which label the eigenstates of the system. We give a brief review of known quantum systems with monodromy, which include such fundamental systems as the hydrogen atom in external fields, Fermi resonant vibrations of the CO/sub 2/ molecule, and non-rigid triatomic molecules. We emphasize the correspondence between the classical Hamiltonian monodromy and its quantum analogue and discuss possible generalizations of this characteristic in classical integrable Hamiltonian dynamical systems and their quantum counterparts
KW - Fermi resonance
KW - quantum monodromy
KW - Specific calculations and results for atoms and molecules
KW - Vibrational analysis molecular spectra
ID - Sadovskii2006DS-mphmon-review
ER -
TY - JOUR
TI - Fractional Hamiltonian monodromy
AU - Nekhoroshev,N.N.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Annales Henri Poincare
JO - Ann.H.Poincar\'e
VL - 7
IS - 6
PY - 2006///
SP - 1099
EP - 211
PB - Birkh\"auser Verlag
U1 - 10.1007/s00023-006-0278-4
AB - We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy-momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:(-2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems
KW - classical mechanics
KW - matrix algebra
KW - nonlinear dynamical systems
KW - oscillators
KW - quantum theory
KW - Foundations, theory of quantum measurement, miscellaneous quantum theories
KW - Nonlinear dynamical systems and bifurcations
KW - Algebra, set theory, and graph theory
KW - Classical mechanics of discrete systems: general mathematical aspects
ID - Nekhoroshev2006DS-fracmono-big
ER -
TY - JOUR
TI - Classical and quantum-mechanical plane switching in {CO}$_2$
AU - Sanrey,M.
AU - Joyeux,M.
AU - Sadovskii,D.A.
JF - Journal of Chemical Physics
JO - J.Chem.Phys.
VL - 124
IS - 7
PY - 2006/02/21/
SP - 74318-1
EP - 12
PB - AIP
U1 - 10.1063/1.2167747
AB - Classical plane switching takes place in systems with a pronounced 1:2 resonance, where the degree of freedom with the lowest frequency is doubly degenerate. Under appropriate conditions, one observes a periodic and abrupt precession of the plane in which the doubly degenerate motion takes place. In this article, we show that quantum plane switching exists in CO/sub 2/. Based on our analytical solutions of classical Hamilton's equations of motion, we describe the dependence on vibrational angular momentum and energy of the frequency of switches and the plane switching angle. Using these results, we find optimal initial wave-packet conditions for CO/sub 2/ and show, through quantum-mechanical propagation, that such a wave packet indeed displays plane switching at energies around 10000 cm$^{-1}$ above the ground state on time scales of about 100 fs
KW - carbon dioxide
KW - Fermi resonance
KW - quantum monodromy
KW - vibrational states and polyades
KW - Specific calculations and results for atoms and molecules
KW - Molecular rotation, vibration, and vibration rotation constants
ID - Sanrey2006DS-CO2-monodromy
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/switchCO2.txt
L1 - /home/dima/public_html/preprints/JCP_124_74318_2006.pdf
ER -
TY - JOUR
TI - Assigning vibrational polyads using relative equilibria: application to ozone
AU - Kozin,I.N.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Spectrochimica Acta, Part A Molecular and Biomolecular Spectroscopy
JO - Spectrochim.Acta A
VL - 61
IS - 13-14
PY - 2005/10//
SP - 2867
EP - 85
PB - Elsevier
U1 - 10.1016/j.saa.2004.10.039
AB - We demonstrate how relative equilibria of a vibrating molecule, which are families of principal periodic orbits otherwise known as nonlinear normal modes, can be used to describe the global polyad structure of vibrational energy levels. The classical action integral n (E) computed along these orbits at different energies E corresponds to the polyad quantum number n so that the energy E (n) of different relative equilibria describes the splitting of n-polyads. Further information on the internal polyad structure can be driven from the stability analysis of relative equilibria. We use the ozone molecule as a concrete example where n-polyads or "hyperpolyads" should be distinguished from the well-known polyads of the 1:1 stretching mode resonance; the stretching polyads are structural elements of hyperpolyads. We give dynamical interpretation of the relation between relative equilibria and n-polyads based on the normal form reduction in the limit of small vibrations near the equilibrium. [All rights reserved Elsevier]
KW - ozone
KW - nonlinear normal mode
KW - relative equilibrium
KW - vibrational polyade
KW - Vibrational analysis molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
KW - Specific calculations and results for atoms and molecules
ID - Sadovskii2005DS-O3-vib-RE
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/ozone.ps.gz
L1 - /home/dima/public_html/preprints/ozone.ps.gz
ER -
TY - CHAP
TI - No Polar Coordinates. Lectures by {R}ichard {C}ushman
AU - Efstathiou,K.
AU - Sadovskii,D.A.
N2 - MASIE Summer School, September, 2000
BT - Geometric Mechanics and Symmetry. The Peyresq Lectures
T3 - London Mathematical Society Lecture Note Series No. 306
N1 - Contents: 1. Stability in Hamiltonian systems: applications to the restricted three-body problem by Meyer,K.R., Rink,B. and Tuwankotta,T.; 2. A crash course in geometric mechanics: Ratiu,T.S., Sousa Dias,E., Sbano,L., Terra,G. and Tudoran,R.; 3. The Euler-Poincaré variational framework for modeling fluid dynamics by Holm,D.D.; 4. No polar coordinates by Cushman,R.H., Sadovskii,D.A. and Efstanthiou,K.; 5. Survey on dissipative KAM theory including quasi-periodic bifurcation theory by Broer,H., Ciocci,M.-C. and Litvak-Hinenzon,A.; 6. Symmetric Hamiltonian bifurcations by Buono,P.-L., Laurent-Polz,F. and Montaldi,J. 412 pages.
A2 - Montaldi,James
A2 - Ratiu,Tudor
SP - 211
EP - 302
PY - 2005/06//
PB - Cambridge University Press
CY - Cambridge, UK
SN - 978-0521539579
ID - Efstathiou2005DS-lnotes
UR - http://us.cambridge.org/titles/catalogue.asp?isbn=0521539579
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/lnotes-Cushman.ps.gz
L1 - /home/dima/public_html/preprints/lnotes-Cushman.ps.gz
ER -
TY - JOUR
TI - Monodromy of the quantum $1{:}1{:}2$ resonant swing spring
AU - Giacobbe,A.
AU - Cushman,R.H.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Journal of Mathematical Physics
JO - J.Math.Phys.
VL - 45
IS - 12
PY - 2004/12//
SP - 5076
EP - 100
PB - AIP
U1 - 10.1063/1.1811788
AB - We describe the qualitative features of the joint spectrum of the quantum 1:1:2 resonant swing spring. The monodromy of the classical analogue of this problem is studied in Dullin et al. [Physica D 190, 15-37 (2004)]. Using symmetry arguments and numerical calculations we compute its three-dimensional (3D) lattice of quantum states and show that it possesses a codimension 2 defect characterized by a nontrivial 3D-monodromy matrix. The form of the monodromy matrix is obtained from the lattice of quantum states and depends on the choice of an elementary cell of the lattice. We compute the quantum monodromy matrix, that is the inverse transpose of the classical monodromy matrix. Finally we show that the lattice of quantum states for the 1:1:2 quantum swing spring can be obtained-preserving the symmetries-from the regular 3D-cubic lattice by means of three "elementary monodromy cuts"
KW - resonant harmonic oscillators
KW - lattice defect theory
KW - quantum monodromy
KW - energy-momentum map
KW - singular reduction
KW - Algebraic methods in quantum theory
KW - Group theory
ID - Giacobbe2004DS-qswing-spring
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/qsspring.pdf
L1 - /home/dima/public_html/preprints/qsspring.pdf
ER -
TY - JOUR
TI - Hamiltonian {H}opf bifurcation of the hydrogen atom in crossed fields
AU - Efstathiou,K.
AU - Cushman,R.H.
AU - Sadovskii,D.A.
JF - Physica D
VL - 194
IS - 3-4
PY - 2004/07/15/
SP - 250
EP - 74
PB - Elsevier
U1 - 10.1016/j.physd.2004.03.003
AB - We consider the hydrogen atom in crossed electric and magnetic fields. We prove that near the Stark and Zeeman limits the system goes through two qualitatively different Hamiltonian Hopf bifurcations. We explain in detail the geometry of the bifurcations
KW - perturbed neutral hydrogen atom
KW - perturbed Kepler system
KW - quantum and classical monodromy
KW - energy-momentum map
KW - singular reduction
KW - normal form
KW - Nonlinear dynamical systems and bifurcations
KW - Stark effect in atoms
KW - Zeeman effect in atoms
ID - Efstathiou2004DS-HHopf-Hatom
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/Hatom-HH-PhysD194-2004p250.txt
L1 - /home/dima/public_html/preprints/Hatom-HH-PhysD194-2004p250.pdf
ER -
TY - JOUR
TI - {CO}$_2$ molecule as a quantum realization of the $1{:}1{:}2$ resonant swing-spring with monodromy
AU - Cushman,R.H.
AU - Dullin,H.R.
AU - Giacobbe,A.
AU - Holm,D.D.
AU - Joyeux,M.
AU - Lynch,P.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Physical Review Letters
JO - Phys.Rev.Lett.
VL - 93
IS - 2
PY - 2004/07/09/
SP - 024302/1
EP - 4
PB - APS
U1 - 10.1103/PhysRevLett.93.024302
AB - We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1:1:2 resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the CO$_2$ molecule. We uncover quantum monodromy of CO$_2$ as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states
KW - carbon dioxide
KW - monodromy
KW - energy-momentum map
KW - singular reduction
KW - elastic pendulum
KW - Fermi resonance
KW - vibrational states and polyades
KW - Vibrational analysis molecular spectra
KW - Classical mechanics of discrete systems
ID - Cushman2004DS-CO2-letter
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/letterCO2.ps.gz
L1 - /home/dima/public_html/preprints/letterCO2.ps.gz
L1 - /home/dima/public_html/preprints/CO2-PRL24302.pdf
ER -
TY - JOUR
TI - Global bending quantum number and the absence of monodromy in the {HCN$\leftrightarrow$CNH} molecule
AU - Efstathiou,K.
AU - Joyeux,M.
AU - Sadovskii,D.A.
JF - Physical Review A Atomic, Molecular, and Optical Physics
JO - Phys.Rev.A
VL - 69
IS - 3
PY - 2004/03//
SP - 32504-1
EP - 15
PB - APS through AIP
U1 - 10.1103/PhysRevA.69.032504
AB - We introduce and analyze a model system based on a deformation of a spherical pendulum that can be used to reproduce large amplitude bending vibrations of flexible triatomic molecules with two stable linear equilibria. On the basis of our model and the recent vibrational potential [J. Chem. Phys. 115, 3706 (2001)], we analyze the HCN/CNH isomerizing molecule. We find that HCN/CNH has no monodromy and introduce the second global bending quantum number for this system at all energies where the potential is expected to work. We also show that LiNC/LiCN is a qualitatively different system with monodromy
KW - spherical pendulum
KW - energy-momentum map
KW - vibrational states and polyades
KW - Vibrational analysis molecular spectra
KW - Classical mechanics of discrete systems: general mathematical aspects
KW - Isomerization and rearrangement
KW - General molecular conformation and symmetry
ID - Efstathiou2004DS-HCN-monodromy
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/HCN-paper.ps.gz
UR - http://purple.univ-littoral.fr/~dima/preprints/HCN-paper.pdf
ER -
TY - JOUR
TI - Perturbations of the {$1{:}1{:}1$} resonance with tetrahedral symmetry: a three degree of freedom analogue of the two degree of freedom {H}\'enon-{H}eiles Hamiltonian
AU - Efstathiou,K.
AU - Sadovskii,D.A.
JF - Nonlinearity
VL - 17
IS - 2
PY - 2004/03//
SP - 415
EP - 46
PB - IOP Publishing; London Math.Soc
U1 - 10.1088/0951-7715/17/2/003
AB - We study a class of three degree of freedom (3-DOF) Hamiltonian systems that share certain characteristics with the 2-DOF Henon-Heiles Hamiltonian. Our systems represent a 1:1:1 resonant three-oscillator whose principal nonlinear perturbation is the cubic potential term xyz with tetrahedral symmetry. After normalizing and reducing the 1:1:1 oscillator symmetry, we show that near the limit of linearization all our systems can be described as a one-parametric family. Such reduced systems have been suggested earlier by Hecht (1960 J. Mol. Spectrosc. 5 355) and later by Patterson (1985 J. Chem.Phys. 83 4618) to model triply degenerate vibrations of tetrahedral molecules. We describe relative equilibria (RE) of these systems, classify all qualitatively different family members, and discuss bifurcations of RE involved in the transitions from one region of regular parameter values to the other
KW - resonant harmonic oscillator
KW - perturbation theory
KW - singular reduction
KW - Nonlinear dynamical systems and bifurcations
ID - Efstathiou2004DS-HH-3D
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/3DHH-cp2.ps.gz
L1 - /home/dima/public_html/preprints/3DHH-cp2.txt
ER -
TY - JOUR
TI - Analysis of rotation-vibration relative equilibria on the example of a tetrahedral four atom molecule
AU - Efstathiou,K.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - SIAM Journal on Applied Dynamical Systems (SIADS)
JO - SIAM J.Appl.Dyn.Syst.
A2 - Holm,Darryl
VL - 3
IS - 3
SP - 261
EP - 351
PY - 2004///
U1 - 10.1137/030600015
AB - We study relative equilibria (RE) of a nonrigid molecule which vibrates about a well defined equilibrium configuration and rotates as a whole. Our analysis unifies the theory of rotational and vibrational RE. We rely on the detailed study of the symmetry group action on the initial and reduced phase space of our system and consider the consequences of this action for the dynamics of the system. We develop our approach on the concrete example of a four-atomic molecule $A_4$ with tetrahedral equilibrium configuration, a dynamical system with six vibrational degrees of freedom. Further applications and illustrations of our results can be found in [Van Hecke, et al, Eur.Phys.J.D 17, 13 (2001)]. Supported by the EU project Mechanics and Symmetry in Europe (MASIE), contract HPRN-CT-2000-00113.
N1 - submitted 23 January 2003, accepted 3 October 2003; ms\#060001
KW - small vibrations
KW - vibration-rotation of molecules
KW - spherical top
KW - relative equilibria
KW - 1:1:1 resonant oscillator
KW - normalization
KW - reduction
KW - bifurcations
KW - orbit space
KW - finite group action
KW - reversing symmetry
KW - Molien generating function
KW - integrity basis
M2 - 37J15, 37J35, 37J40, 81V55, 58D19
ID - Efstathiou2004DS-A4-vibrot-theory
UR - http://epubs.siam.org/sam-bin/dbq/article/60001
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/CP2S2.ps.gz
UR - http://purple.univ-littoral.fr/~dima/preprints/cp2s2.pdf
L1 - /home/dima/public_html/preprints/SIADS-60001-v3p261-351.pdf
L3 - /home/dima/public_html/preprints/CP2S2.txt
ER -
TY - JOUR
TI - Linear {H}amiltonian {H}opf bifurcation for point-group-invariant perturbations of the $1{:}1{:}1$ resonance
AU - Efstathiou,K.
AU - Sadovskii,D.A.
AU - Cushman,R.H.
JF - Proceedings of the Royal Society of London, Series A Mathematical, Physical and Engineering Sciences
JO - Proc.Roy.Soc.A
VL - 459
IS - 2040
PY - 2003/12/08/
SP - 2997
EP - 3019
PB - Royal Society London
U1 - 10.1098/rspa.2003.1158
AB - We consider GxR-invariant Hamiltonians H on complex projective 2-space, where G is a point group and R is the time-reversal group. We find the symmetry-induced stationary points of H and classify them in terms of their linear stability. We then determine those points that can undergo a linear Hamiltonian Hopf bifurcation
KW - linear stability
KW - relative equilibrium
KW - perturbation theory
KW - Nonlinear dynamical systems and bifurcations
KW - Group theory
ID - Efstathiou2003DS-CP2-local-study
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/lHHb.ps.gz
ER -
TY - JOUR
TI - Monodromy of the {LiNC/NCLi} molecule
AU - Joyeux,M.
AU - Sadovskii,D.A.
AU - Tennyson,J.
JF - Chemical Physics Letters
JO - Chem.Phys.Lett.
VL - 382
IS - 3-4
PY - 2003/12/05/
SP - 439
EP - 42
PB - Elsevier
U1 - 10.1016/j.cplett.2003.10.099
AB - Using the potential surface of Essers, Tennyson, and Wormer, we show that the system of bending vibrational states of the isomerizing molecule LiNC/NCLi has monodromy. On the basis of a deformed spherical pendulum model, we explain dynamical and geometric reasons of this phenomenon and of its absence in the similar system HCN/CNH
KW - lithium compounds
KW - quantum monodromy
KW - energy-momentum map
KW - spherical pendulum
KW - potential energy surfaces
KW - vibrational states and polyades
KW - General molecular conformation and symmetry
KW - Molecular rotation, vibration, and vibration rotation constants
KW - Molecular bond strengths, dissociation energies, hydrogen bonding
ID - Joyeux2003DS-LiNC-monodromy
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/LiNC-letter.ps.gz
L1 - /home/dima/public_html/preprints/LiNC-letter.pdf
ER -
TY - JOUR
TI - Fractional monodromy of resonant classical and quantum oscillators
AU - Nekhoroshev,N.N.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Comptes Rendus de l'Academie des Sciences, Serie I Mathematique
VL - 335
IS - 11
PY - 2002/12/01/
SP - 985
EP - 8
PB - Elsevier
AB - We introduce fractional monodromy for a class of integrable fibrations which naturally arise for classical nonlinear oscillator systems with resonance. We show that the same fractional monodromy characterizes the lattice of quantum states in the joint spectrum of the corresponding quantum systems. Results are presented on the example of a two-dimensional oscillator with resonance 1:(-1) and 1:(-2)
KW - resonance, resonant harmonic oscillator
KW - energy-momentum map
KW - lattice defect theory
KW - quantum monodromy
KW - Classical mechanics of discrete systems: general mathematical aspects
KW - Nonlinear dynamical systems and bifurcations
KW - Semiclassical theories and applications in quantum theory
ID - Nekhoroshev2002DS-drobmono
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/drobmono-cras-preprint.ps.gz
L1 - /home/dima/public_html/preprints/drobmono-cras.ps.gz
ER -
TY - JOUR
TI - Monodromy as topological obstruction to global action-angle variables in systems with coupled angular momenta and rearrangement of bands in quantum spectra
AU - Grondin,L.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Physical Review A Atomic, Molecular, and Optical Physics
JO - Phys.Rev.A
VL - 65
IS - 1
PY - 2002/01//
SP - 012105/1
EP - 15
PB - APS through AIP
U1 - 10.1103/PhysRevA.65.012105
AB - We continue to study the relation between the redistribution of levels in quantum energy spectra and monodromy of the corresponding classical system [see Phys.Lett.A 256, 235 (1999)]. A system with two coupled angular momenta and SO(2) symmetry is compared to a system with three momenta and SO(3) symmetry
KW - angular momentum
KW - energy-momentum map
KW - quantum monodromy
KW - theory of lattice defects
KW - Group theory, SO(2) and SO(3) groups
KW - Semiclassical theories and applications in quantum theory
ID - Grondin2002DS-threeL
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/lucien.ps.gz
L1 - /home/dima/public_html/preprints/lucien.txt
ER -
TY - JOUR
TI - Rotational-vibrational relative equilibria and the structure of quantum energy spectrum of the tetrahedral molecule {P}$_4$
AU - Van-Hecke,C.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
AU - Boudon,V.
JF - European Physical Journal D
JO - Europ.Phys.J.D
VL - 17
IS - 1
PY - 2001/10//
SP - 13
EP - 35
PB - EDP Sciences; Springer-Verlag
AB - We find relative equilibria (RE) of the rotating and vibrating tetrahedral molecule P$_4$ and study the correspondence of these RE's to the extremal quantum states in the vibration-rotation multiplet and to the extrema of the semi-quantum rotational energy surfaces obtained for a number of excited vibrational states. To compute the energy of RE's we normalize the full rotation-vibration Hamiltonian H of P$_4$ in the approximation of nonresonant modes $\nu_2$/sup E/ and nu /sub 3/(F$_2$) and find the stationary points of the resulting normal form (known as reduced effective Hamiltonian H/sub eff/) which is defined on the reduced phase space CP$_2$ x CP/sub 1/ x S$_2$. Most of these points are fixed points of the symmetry group action on CP$_2$ x CP/sub 1/ x S$_2$. To explain our results in more detail we introduce numerical values of the parameters of H, such as the cubic force constants, using an atom-atom harmonic potential with one adjustable parameter. This simple model gives correct qualitative description of the rotational structure of the lowest excited vibrational states $\nu_2$, nu /sub 3/ and $\nu_2$ + nu /sub 3/ of P$_4$
KW - molecular force constants
KW - phosphorus
KW - rotational vibrational states and polyades
KW - Vibrational rotational analysis molecular spectra
ID - van-Hecke2001DS-P4rovib
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/P4rovib.ps.gz
L1 - /home/dima/public_html/preprints/P4rovib.txt
ER -
TY - CHAP
TI - Normal forms, geometry, and dynamics of atomic and molecular systems with symmetry
AU - Sadovskii,D.A.
N2 - Erratum: eq.(1) must read \(H = H_0 + \epsilon V(q) = \tfrac12(p_x^2+q_x^2) + \tfrac12(p_y^2+q_y^2) + \epsilon (\frac13 q_x^3 - q_x q_y^2)\)
SP - 191
EP - 205
BT - Symmetry and Perturbation Theory (SPT2001)
N1 - Proceedings of the international conference, Cala Gonone, Sardinia, Italy 6--13 May 2001
A2 - Bambusi,D.
A2 - Cadoni,M.
A2 - Gaeta,G.
PY - 2001/10//
PB - World Scientific
CY - Singapore
SN - 981-02-4793-1
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/spt2001.ps.gz
UR - http://purple.univ-littoral.fr/~dima/preprints/spt2001-talk.ps.gz
L1 - ~/biblio/dima/"Bahbusi D., et al. (eds.) Symmetry and perturbation theory. Proc. int. conf., Italy 2001 (WS, 2001)(ISBN 9810247931)(260s)_MP_.pdf"
ID - Sadovskii2001DS-SPT2001
ER -
TY - JOUR
TI - Monodromy in the hydrogen atom in crossed fields
AU - Cushman,R.H.
AU - Sadovskii,D.A.
JF - Physica D
VL - 142
IS - 1-2
PY - 2000/08/01/
SP - 166
EP - 96
U1 - 10.1016/S0167-2789(00)00053-1
PB - Elsevier
AB - We show that the hydrogen atom in orthogonal electric and magnetic fields has a special property of certain integrable classical Hamiltonian systems known as monodromy. The strength of the fields is assumed to be small enough to validate the use of a truncated normal form H/sub snf/ which is obtained from a two step normalization of the original system. We consider the level sets of H/sub snf/ on the second reduced phase space. For an open set of field parameters we show that there is a special dynamically invariant set which is a "doubly pinched 2-torus". This implies that the integrable Hamiltonian H/sub snf/ has monodromy. Manifestation of monodromy in quantum mechanics is also discussed
KW - atomic structure
KW - hydrogen neutral atom
KW - Zeeman and Stark effect
KW - Kustaanheimo-Stiefel regularization
KW - SO(4) dynamical symmetry group
KW - normal form
KW - singular reduction
KW - energy-momentum map
KW - quantum monodromy
KW - quantisation quantum theory
KW - General mathematical and computational developments for atoms and molecules
KW - Semiclassical theories and applications in quantum theory
ID - Cushman2000DS-monodromy-cf-detailed
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/mndr-PhysicaD.ps.gz
L1 - /home/dima/public_html/preprints/mndr-PhysicaD142p166-2000.pdf
ER -
TY - JOUR
TI - Analysis of the `unusual' vibrational components of triply degenerate vibrational mode $\nu_6$ of {Mo(CO)}$_6$ based on the classical interpretation of the effective rotation-vibration Hamiltonian
AU - Dhont,G.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
AU - Boudon,V.
JF - Journal of Molecular Spectroscopy
JO - J.Mol.Spectrosc.
VL - 201
IS - 1
PY - 2000/05//
SP - 95
EP - 108
PB - Academic Press
U1 - 10.1006/jmsp.2000.8070
AB - Rotational structure of the triply degenerate vibrational state nu /sub 6/(F/sub 1u/) of the octahedral molecule Mo(CO)/sub 6/ is analyzed qualitatively on the basis of classical mechanics. We show that the energy level redistribution between the vibrational components of nu /sub 6/(F/sub 1u/) occurs due to rotational excitation and is related to the formation of singular points of classical rotational energy surfaces. The singularity is stable under small variations of parameters of the effective rovibrational Hamiltonian. Parameters responsible for the persistence of this phenomenon are specified. Comparison with quantum calculations demonstrates the high qualitative and quantitative accuracy of our classical analysis
KW - molybdenum compounds
KW - rotational vibrational states
KW - Vibrational rotational analysis molecular spectra
ID - Dhont2000DS-MoCO6
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/MoCO6paper.ps.gz
ER -
TY - JOUR
TI - Qualitative analysis of molecular rotation starting from inter-nuclear potential
AU - Van-Hecke,C.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - European Physical Journal D
JO - Europ.Phys.J.D
VL - 7
IS - 2
PY - 1999/09//
SP - 199
EP - 209
PB - EDP Sciences; Springer-Verlag
AB - We study how qualitative features of the molecular rotational dynamics can be derived directly from the internuclear (vibrational) potential. This approach is presented on the example of a tetrahedral molecule A$_4$ using several increasingly elaborated models of the potential
KW - potential energy functions
KW - potential energy surfaces
KW - rotational vibrational states and polyades
KW - Semiclassical theories and applications in quantum theory
KW - Vibrational rotational analysis molecular spectra
ID - Van-Hecke1999DS-vanhecke
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/A4RES.ps.gz
L1 - /home/dima/public_html/preprints/A4RES.txt
ER -
TY - JOUR
TI - Monodromy in perturbed Kepler systems: hydrogen atom in crossed fields
AU - Cushman,R.H.
AU - Sadovskii,D.A.
JF - Europhysics Letters
JO - Europhys.Lett.
VL - 47
IS - 1
PY - 1999/07/01/
SP - 1
EP - 7
PB - Eur.Phys.Soc. by EDP Sciences and Soc.Italiana Fisica
AB - We demonstrate that an integrable approximation to the hydrogen atom in orthogonal electric and magnetic fields has monodromy, a fundamental dynamical property that makes a global definition of action-angle variables and of quantum numbers impossible. When the field strengths are sufficiently small, we find our integrable approximation using a two step normalization procedure. One of dynamically invariant sets of the resulting integrable system is a doubly pinched torus whose existence proves the presence of monodromy
KW - hydrogen neutral atom
KW - many body problems
KW - perturbation theory
KW - quantum theory
KW - energy-momentum map
KW - Stark effect in atoms
KW - Zeeman effect in atoms
KW - Semiclassical theories and applications in quantum theory
KW - Classical mechanics of discrete systems: general mathematical aspects
ID - Cushman1999DS-monodromy-cf
RP - IN FILE
U1 - 10.1209/epl/i1999-00341-6
UR - http://purple.univ-littoral.fr/~dima/preprints/mnote-A4.ps.gz
L1 - /home/dima/public_html/preprints/mnote-A4.txt
ER -
TY - JOUR
TI - Monodromy, diabolic points, and angular momentum coupling
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Physics Letters A
JO - Phys.Lett.A
VL - 256
IS - 4
PY - 1999/06/07/
SP - 235
EP - 44
U1 - 10.1016/S0375-9601(99)00229-7
PB - Elsevier
AB - Monodromy, or the most basic obstruction to global action-angle coordinates is shown to be present in the well known problem of two coupled angular momenta. It is also shown that in the corresponding quantum problem monodromy manifests itself as the redistribution of energy levels between different multiplets of the quantum spectrum
KW - angular momentum theory
KW - quantum monodromy
KW - energy-momentum map
KW - Algebraic methods in quantum theory
ID - Sadovskii1999DS-dpnote2
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/dpmnote-A4.ps.gz
L1 - /home/dima/public_html/preprints/dpmnote-A4.txt
ER -
TY - JOUR
TI - Tuning the hydrogen atom in crossed fields between the {Z}eeman and {S}tark limits
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Physical Review A Atomic, Molecular, and Optical Physics
JO - Phys. Rev. A
VL - 57
IS - 4
PY - 1998/04//
SP - 2867
EP - 84
U1 - 10.1103/PhysRevA.57.2867
PB - APS through AIP
AB - We consider the hydrogen atom in the orthogonal electric and magnetic fields whose strength is assumed to be small enough for the Coulomb n-shell perturbation theory to apply. Appropriate scaling of the two fields leads to a uniform parametrization of the problem by S, the combined strength of the two fields, and alpha , the ratio of the two field strengths. The initial six-dimensional phase space R/sub 6/ is lifted to the standard Kustaanheimo-Stiefel eight-dimensional space and then reduced explicitly to the S$_2$xS$_2$ reduced space of the n shell using the Lie transformation to the third order in S. At fixed S the system is uniformly tuned between the Zeeman and the Stark limits using the analytic formulas of the perturbation theory. The approach requires application of the invariant theory, group theory, and topology to the analysis of the dynamics on the reduced space S$_2$xS$_2$ and subsequent explicit transition to the original R/sub 6/. In particular we follow the evolution of the four principal periodic orbits (nonlinear normal modes) and corresponding four relative equilibria on S$_2$xS$_2$
KW - Geometry, differential geometry, and topology
KW - Group theory
KW - SO(4) dynamical symmetry group
KW - hydrogen neutral atom
KW - perturbed Kepler system
KW - Kustaanheimo-Stiefel regularization
KW - normal form
KW - perturbation theory
KW - relative equilibrium
KW - Stark and Zeeman effect in atoms
ID - Sadovskii1998DS-crossed
UR - http://purple.univ-littoral.fr/~dima/preprints/csfield.ps.gz
RP - IN FILE
L1 - /home/dima/public_html/preprints/csfield.txt
ER -
TY - JOUR
TI - Spectra of rare gas hydrides. {VI}. The $4f$ complex and the electronic structure of {KrD}
AU - Dabrowski,I.
AU - Sadovskii,D.A.
JF - Journal of Chemical Physics
JO - J.Chem.Phys.
VL - 107
IS - 21
PY - 1997/12/01/
SP - 8874
EP - 85
U1 - 10.1063/1.475179
PB - AIP
AB - The complete rotational analysis of the 4f(/sup 2/ Phi , /sup 2/ Delta , /sup 2/pi, /sup 2/ Sigma /sup +/)to4d/sup 2/ Delta (6600 cm$^{-1}$), 4f(/sup 2/ Phi , /sup 2/ Delta , /sup 2/pi, /sup Sigma +/)to4d/sup 2/pi (8500 cm$^{-1}$), and 4d/sup 2/ Delta to5p /sup 2/pi (7100 cm$^{-1}$) Rydberg electronic transitions of KrD is reported. The two newly observed states, the doublet 4f complex and 4d/sup 2/ Delta together with the np(/sup 2/pi, /sup 2/ Sigma /sup +/), nd /sup 2/ Sigma /sup +/, ns /sup 2/ Sigma /sup +/, and nd /sup 2/pi studied earlier by Dabrowski et al., [Mol. Phys. 63, 269 (1988)], and by Dabrowski and Sadovskii [Mol.Phys. 81, 291 (1994)], form a set of states which permits the whole Rydberg electronic structure of the molecule to be determined from the experimental data
KW - molecular Rydberg electronic states
KW - rotational structure electronic molecular states
KW - Infrared molecular spectra
KW - Rotational analysis electronic molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
ID - Debrowski1997DS-KrD-f
ER -
TY - JOUR
TI - Bifurcation of the periodic orbits of {H}amiltonian systems: an analysis using normal form theory
AU - Sadovskii,D.A.
AU - Delos,J.B.
JF - Physical Review E Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JO - Phys.Rev.E
VL - 54
IS - 2
PY - 1996/08//
SP - 2033
EP - 70
PB - APS / AIP
AB - We develop an analytic technique to study the dynamics in the neighborhood of a periodic trajectory of a Hamiltonian system. The theory begins with Poincare and Birkhoff; major modern contributions are due to Meyer, Arnol'd, and Deprit. The realization of the method relies on local Fourier-Taylor series expansions with numerically obtained coefficients. The procedure and machinery are presented in detail on the example of the "perpendicular" (z=0) periodic trajectory of the diamagnetic Kepler problem. This simple one-parameter problem well exhibits the power of our technique. Thus, we obtain a precise analytic description of bifurcations observed by J.-M. Mao and J.B. Delos [Phys.Rev. A 45, 1746 (1992)] and explain the underlying dynamics and symmetries
KW - Lie algebra, Lie transform
KW - perturbation theory
KW - normal form
KW - Nonlinear dynamical systems and bifurcations
ID - Sadovskii1996DS-nf-PT
U1 - 10.1103/PhysRevE.54.2033
RP - IN FILE
UR - http://purple.univ-littoral.fr/~dima/preprints/nf-PT.ps.gz
ER -
TY - JOUR
TI - Collapse of the {Z}eeman structure of the hydrogen atom in an external electric field
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
AU - Michel,L.
JF - Physical Review A Atomic, Molecular, and Optical Physics
JO - Phys.Rev.A
VL - 53
IS - 6
PY - 1996/06//
SP - 4064
EP - 4067
PB - APS via AIP
AB - We analyze the transition from a Zeeman to a Stark structure of a weakly split Rydberg $n$ multiplet of the H atom in parallel magnetic and electric fields. The use of classical mechanics, topology, and group theory provides a detailed description of the modifications of dynamics due to the variation of the electric field. We focus on the point where the collapse of the Zeeman structure occurs, give the sequence of classical bifurcations responsible for the transition between different dynamic regimes, and compare it to the quantum energy-level structure
N2 - this paper was first submitted to PRL and took several years to publish
KW - Group theory
KW - hydrogen neutral atom
KW - Rydberg states
KW - Zeeman effect in atoms
KW - Stark effect in atoms
ID - Sadovskii1996DS-collapse
RP - IN FILE
U1 - 10.1103/PhysRevA.53.4064
UR - http://purple.univ-littoral.fr/~dima/preprints/Collapse.ps.gz
L1 - /home/dima/public_html/preprints/PRA53p4064-1996.pdf
ER -
TY - JOUR
TI - Counting levels within vibrational polyads: generating function approach
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Journal of Chemical Physics
JO - J.Chem.Phys.
VL - 103
IS - 24
PY - 1995/12/22/
SP - 10520
EP - 36
U1 - 10.1063/1.469836
PB - AIP
AB - Simple analytical formulas for the number of energy levels in the vibrational polyads are given. These formulas account for the resonances between the vibrational modes, and for the symmetry of the problem, so that the number of states of a particular symmetry type can be computed. The formulas are used to estimate the differential and integral densities of states from the minimum initial information about the molecule. Examples of the vibrational structure of triatomic molecules A/sub 3/, tetrahedral molecules AB$_4$, and linear molecules AB$_2$ are considered. The analytical formulas are compared to the ab initio results for H$_3^+$ [J.R. Henderson et al., J.Chem.Phys. 98, 7191 (1993)]
KW - density of states
KW - resonant harmonic oscillator
KW - vibrational polyades
KW - invariant theory
KW - generating fumction
KW - General mathematical and computational developments for atoms and molecules
KW - Vibrational analysis molecular spectra
ID - Sadovskii1995DS-polyads
UR - http://purple.univ-littoral.fr/~dima/preprints/Polyads.ps.gz
RP - IN FILE
L1 - /home/dima/public_html/preprints/Polyads.ps.gz
ER -
TY - JOUR
TI - Organization of sequences of bifurcations of periodic orbits
AU - Sadovskii,D.A.
AU - Shaw,J.A.
AU - Delos,J.B.
JF - Physical Review Letters
JO - Phys.Rev.Lett.
VL - 75
IS - 11
PY - 1995/09/11/
SP - 2120
EP - 3
U1 - 10.1103/PhysRevLett.75.2120
AB - Numerical calculations have shown that bifurcations of periodic orbits of Hamiltonian systems often occur in organized groups. Normal-form theory provides an explanation
KW - perturbation theory
KW - normal form
KW - Nonlinear dynamical systems and bifurcations
ID - Sadovskii1995DS-PT-lett
UR - http://purple.univ-littoral.fr/~dima/preprints/nf-prl.ps.gz
UR - http://purple.univ-littoral.fr/~dima/preprints/PRL75p2120-1995.djvu
RP - IN FILE
L1 - /home/dima/public_html/preprints/nf-prl.ps.gz
L1 - /home/dima/public_html/preprints/PRL75p2120-1995.djvu
ER -
TY - JOUR
TI - New observations and analysis of the infrared vibration-rotation spectrum of {H}$_3^+$
AU - Majewski,W.A.
AU - McKellar,A.R.W.
AU - Sadovskii,D.A.
AU - Watson,J.K.G.
JF - Canadian Journal of Physics
JO - Can.J.Phys.
VL - 72
IS - 11-12
PY - 1994/11//
SP - 1016
EP - 27
AB - The coverage of the infrared spectrum of the H$_3^+$ molecular ion is extended by further measurements of the emission from a small high-pressure hollow-cathode electrical discharge cell, using the pressure dependence of the intensities to distinguish the lines of H$_3^+$ from the many lines due to electronic transitions of H$_2$ in the same region. The lines were assigned by means of calculations with a large vibration-rotation basis, using a Morse-based discrete variable representation for the vibrations. Eight coefficients in the Meyer-Botschwina-Burton ab initio potential were adjusted in order to fit 621 lines of H$_3^+$ from this and previous work with a standard deviation of 0.118 cm$^{-1}$
KW - triatomic hydrogen
KW - positive molecular ions
KW - rotational vibrational states
KW - Infrared molecular spectra
KW - Vibrational rotational analysis molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
KW - Molecular lifetimes, absolute and relative line and band intensities
ID - Majewski1994DS-H3pHIA
ER -
TY - JOUR
TI - The infrared vibration-rotation spectrum of the {D}$_3^+$ molecular ion: extension to higher vibrational and rotational quantum numbers
AU - Amano,T.
AU - Chan,M.C.
AU - Civis,S.
AU - McKellar,A.R.W.
AU - Majewski,W.A.
AU - Sadovskii,D.A.
AU - Watson,J.K.G.
JF - Canadian Journal of Physics
JO - Can.J.Phys.
VL - 72
IS - 11-12
PY - 1994/11//
SP - 1007
EP - 15
AB - The assigned infrared spectrum of the D$_3^+$ molecular ion is extended from 84 to 529 lines by three types of spectroscopic measurements on hollow-cathode electrical discharges through deuterium gas: (i) emission from a small hollow cathode, in which the D$_3^+$ lines were distinguished from the electronic transitions of D$_2$ by the pressure dependence of their intensities; (ii) absorption in the same hollow cathode with discharge amplitude modulation; and (iii) absorption in a larger hollow cathode cell with discharge amplitude modulation. The observed lines being mainly to the $\nu_2$/sup 1/-0 fundamental and its hot bands 2 $\nu_2$/sup 0/- $\nu_2$/sup 1/, 2 $\nu_2$/sup 2/- $\nu_2$/sup 1/ and nu /sub 1/+ $\nu_2$/sup 1/- nu /sub 1/ in the 1330-2530 cm$^{-1}$ region in experiments (i) and (ii), and to the first overtone band 2 $\nu_2$/sup 2/-0 in the 3160-4000 cm$^{-1}$ region in experiment (iii). The lines were assigned by means of calculations with a large vibration-rotation basis, using a Morse-based discrete variable representation for the vibrations. This method overcomes the convergence problems for the centrifugal terms in the effective Hamiltonian approach. Six coefficients in the Meyer-Botschwina-Burton ab initio potential were adjusted in order to fit these data with a standard deviation of 0.059 cm$^{-1}$
KW - deuterium
KW - positive molecular ions
KW - rotational vibrational states
KW - Infrared molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
ID - Amano1994DS-D3pHIA
ER -
TY - JOUR
TI - Spectra of the rare gas hydrides. {V}. The $np$ {R}ydberg series of {KrD}
AU - Dabrowski,I.
AU - Sadovskii,D.A.
JF - Molecular Physics
JO - Mol.Phys.
VL - 81
IS - 2
PY - 1994/02/10/
SP - 291
EP - 326
U1 - 10.1080/00268979400100201
AB - The 23920 cm$^{-1}$, 21950 cm$^{-1}$, and 17840 cm$^{-1}$ emission bands of KrD have been analysed successfully as transitions from the 8p, 7p, and 6p Rydberg complexes to the lowest bound state, /sup 2/ Sigma . It was found that the structure of these states corresponds to a special case of l uncoupling with a Coriolis-like linear dependence of the case (d) electron-rotation energies on the quantum number R. The structure of the lowest member of the series, the 5p(/sup 2/ Sigma ,/sup 2/pi) complex, has been obtained from the simultaneous analysis of the 5050 cm$^{-1}$ and 5800 cm$^{-1}$ emission bands as transitions from the 4d/sup 2/pi case (b) upper state to the 5p/sup 2/ Sigma and 5p/sup 2/pi components of the complex. The latter are widely split, E/sub pi/-E/sub Sigma /=735 cm$^{-1}$ due to electronic interactions and are further distorted by strong spin-orbit interactions. The 5p(/sup 2/ Sigma ,/sup 2/pi) complex corresponds to the p complex of ArD studied recently by Dabrowski et al. (1992)
KW - krypton compounds
KW - molecular excited electronic states
KW - molecular Rydberg states
KW - spin orbit interactions
KW - visible spectra of diatomic inorganic molecules
ID - Dabrowski1994DS-KrD-p
ER -
TY - JOUR
TI - Qualitative study of a model three-level Hamiltonian with SU(3) dynamical symmetry
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Physical Review A Atomic, Molecular, and Optical Physics
JO - Phys.Rev.A
VL - 48
IS - 2
PY - 1993/08//
SP - 1035
EP - 44
U1 - 10.1103/PhysRevA.48.1035
AB - Bifurcations found by Leboeuf and Saraceno [Phys.Rev. A 41, 4614 (1990)] in a model Hamiltonian system with SU(3) dynamical symmetry are analyzed in terms of a topological, symmetry-adapted approach. The topological structure of the reduced phase space of the problem, a complex projective space in two dimensions, CP$^2$, is used explicitly in the analysis. The study of the action of the finite (additional) symmetry group of the problem leads to a complete classification of stationary solutions and their bifurcations
KW - bifurcation
KW - Algebraic methods in quantum theory
KW - Geometry, differential geometry, and topology
KW - complex projective space
KW - Group theory
KW - SU(3) group
ID - Sadovskii1993DS-CP2
ER -
TY - JOUR
TI - Nonlinear normal modes and local bending vibrations of {H}$_3^+$ and {D}$_3^+$
AU - Sadovskii,D.A.
AU - Fulton,N.G.
AU - Henderson,J.R.
AU - Tennyson,J.
AU - Zhilinskii,B.I.
JF - Journal of Chemical Physics
JO - J.Chem.Phys.
J1 - JCP
VL - 99
IS - 2
PY - 1993/07/15/
SP - 906
EP - 18
AB - The structure of bending overtones of the H$_3^+$ and D$_3^+$ molecular ions at the energies below the barrier to linearity is analyzed using energies and wave functions from full three-dimensional discrete variable representation calculations. The lowest-in-energy states of the vibrational polyads $\nu_2$=4,5,6 are shown to follow the localization pattern of local bending modes, three equivalent-by-symmetry principal periodic trajectories of the corresponding classical two-mode system near the equilibrium
KW - positive triatomic hydrogen and deuterium ions
KW - Nonlinear normal modes
KW - relative equilibria of molecules
KW - molecular energy level calculations
KW - molecular vibration
KW - Specific calculations and results for atoms and molecules
KW - Molecular rotation, vibration, and vibration rotation constants
ID - Sadovskii1993DS-H3plus-vib
ER -
TY - JOUR
TI - Group-theoretical and topological analysis of localized rotation-vibration states
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Physical Review A Atomic, Molecular, and Optical Physics
JO - Phys.Rev.A
J1 - PRA
VL - 47
IS - 4
PY - 1993/04//
SP - 2653
EP - 71
U1 - 10.1103/PhysRevA.48.1035
AB - A general scheme of qualitative analysis is applied to molecular rovibrational problems. The classical-quantum correspondence provides a description of different classes of localized quantum rotation-vibration states associated with localized classical motion. A description of qualitative features, such as localized motion, and of qualitative changes, such as localization phenomena, is based on the concept of the simplest Hamiltonian. It uses only the topological properties of the compact reduced phase space and the action of the symmetry group on this space. The qualitative changes of the simplest Hamiltonian are analyzed as bifurcations caused by rotational or vibrational excitation. The relation between the stationary points of the classical Hamiltonian function on the reduced phase space and the principal periodic trajectories in the coordinate space is analyzed for vibrational Hamiltonians. In particular, the relation between the nonlinear normal modes, proposed by Montaldi, Roberts, and Stewart [Philos. Trans.R.Soc. London, Ser.A 325, 237 (1988)], and normal- and local-mode models widely used in molecular physics is discussed. Along with a general consideration of localized rotational and vibrational states a more detailed analysis of the vibrational dynamics of an X/sub 3/ molecule with the D/sub 3h/ symmetry, such as the H$_3^+$ molecular ion, is given
KW - Group theory
KW - molecular rotation vibration calculations
KW - Vibrational rotational analysis molecular and atomic spectra
ID - Sadovskii1993DS-gt-analysis
ER -
TY - JOUR
TI - Study of the $\nu_1$, $\nu_3$ bands of $^{120}${SnH}$_4$. {II}. {S}emiclassical qualitative analysis: critical phenomena and diabolic points
AU - Krivtsun,V.M.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Proceedings of the SPIE The International Society for Optical Engineering
VL - 1724
PY - 1992///
SP - 165
EP - 76
AB - For pt.I see ibid., vol.1724, p.148-64 (1992). The qualitative modifications of the rovibrational energy-level structure under rotational excitation are studied for the $\nu_1$, $\nu_3$ bands of $^{120}$SnH$_4$. Two types of qualitative changes exist: the critical phenomena corresponding to the modification of the cluster structure and the so-called diabolic points associated with the redistribution of energy levels between different branches as the rotational quantum number increases. A simple model interpretation of energy-level redistribution is given to show that such a phenomenon is typical for tetrahedral molecules
KW - critical phenomena
KW - molecular rotation vibration calculations
KW - tin compounds
KW - Vibrational rotational analysis molecular spectra
ID - Krivtsun1992DS-31
ER -
TY - JOUR
TI - Study of the $\nu_1$, $\nu_3$ bands of $^{120}${SnH}$_4$. {I}. {D}iode laser spectroscopy
AU - Krivtsun,V.M.
AU - Sadovskii,D.A.
AU - Snegirev,E.P.
JF - Proceedings of the SPIE The International Society for Optical Engineering
VL - 1724
PY - 1992///
SP - 148
EP - 64
AB - An absorption spectrum of the SnH$_4$ molecule has been measured with Doppler limited resolution in the region 1903-60 cm$^{-1}$ by means of a tunable diode laser spectrometer. IR transitions of the Q- and R-branches of allowed $\nu_3$(F$_2$) and `forbidden' $\nu_1$(A$_1$) bands were observed. These two states were strongly mixed by the rotational-vibrational interaction, and as a consequence the $\nu_1$ band appears in absorption. Wavenumbers of transitions to the $\nu_1$, $\nu_3$ energy levels with the quantum number of angular momentum J=1-15 have been obtained with an accuracy of about 0.001 cm$^{-1}$. More than 230 transitions of the $^{120}$SnH$_4$ isotopic species were used for simultaneous analysis of the $\nu_1$, $\nu_3$ resonance states. In this way 21 spectroscopic parameters of the upper states have been determined using a model Hamiltonian, which explicitly takes into account the resonance interaction. The parameters outlined reproduce the experimental spectrum with r.m.s. discrepancy of 0.002 cm$^{-1}$
KW - infrared spectra of polyatomic inorganic molecules
KW - molecular electronic states
KW - molecular rotation vibration
KW - molecular vibration
KW - tin compounds
KW - Infrared molecular spectra
KW - Vibrational analysis molecular spectra
KW - Vibrational rotational analysis molecular spectra
ID - Krivtsun1992DS-32
ER -
TY - JOUR
TI - Spectra of the rare gas hydrides. {IV}. Three new bands of argon deuteride involving a low-lying `$p$' {R}ydberg state
AU - Dabrowski,I.
AU - DiLonardo,G.
AU - Herzberg,G.
AU - Johns,J.W.C.
AU - Sadovskii,D.A.
AU - Vervloet,M.
JF - Journal of Chemical Physics
JO - J.Chem.Phys.
VL - 97
IS - 10
PY - 1992/11/15/
SP - 7093
EP - 110
U1 - 10.1063/1.463535
AB - For part III see Mol.Phys. 65(5), p.1217-25 (1988). Three fairly strong emission bands of ArD at 6100, 6900, and 10200 cm$^{-1}$ have been studied at high resolution. They show very different structures: the first exhibits only Q-form branches, the second P, R, O, and S-form branches, and the third Q, S, and O-form branches. The rotational analysis of each of these bands is not trivial, mainly because the upper state of the first which proved to be also the lower state of the second and third is strongly affected by l uncoupling [i.e., transition to Hund's case (d)] and as a result the usual method of combination differences cannot be applied in their analysis. However, more sophisticated combination differences have been found between the three bands which lead to unambiguous assignments of rotational quantum numbers and thus to rotational constants. It was found that the upper state of the 6100 cm$^{-1}$ band can be most conveniently represented as a $p(^2\Sigma, ^2\Pi)$ complex. This assumption, together with the theoretical selection rules for such a case, led to a full understanding of the structure of the three bands
KW - argon compounds
KW - infrared spectra of diatomic inorganic molecules
KW - molecular excited states
KW - molecular rotation calculations
KW - Infrared molecular spectra
KW - Rotational analysis molecular spectra
KW - Excited states of atoms and molecules
ID - Dabrowski1992DS-ArD-p
RP - IN FILE
L1 - /home/dima/public_html/preprints/JChemPhys_97_7093.djvu
ER -
TY - JOUR
TI - Rotational structure of $^{120}${SnH}$_4$ molecule: $\nu_1$, $\nu_3$ bands
AU - Krivtsun,V.M.
AU - Sadovskii,D.A.
AU - Snegirev,E.P.
JF - Optics and Spectroscopy
JO - Opt.Spectrosc.(USSR)
VL - 70
IS - 5
PY - 1991/05//
SP - 590
EP - 2
AB - The absorption spectrum of the $^{120}$SnH$_4$ molecule has been measured in the 1903-1960-cm$^{-1}$ region with ~10/sup -3/-cm$^{-1}$ resolution using an automated tunable diode laser spectrometer. More than 230 transitions of the $\nu_1$, $\nu_3$ bands for the quantum number values J=1-15 were recorded and their assignment was given by solving the inverse spectroscopic problem. The values of the twenty-one model Hamiltonian parameters thus obtained reproduce the experimental spectrum with a standard deviation of 2x10$^{-3}$ cm$^{-1}$
N2 - in Russian (Optika i Spektroskopiya) pp.1007--10
KW - infrared spectra of polyatomic inorganic molecules
KW - molecular rotation vibration
KW - tin compounds
KW - Infrared molecular spectra
KW - Vibrational rotational analysis molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
ID - Krivtsun1991DS-34
ER -
TY - JOUR
TI - Standard decomposition of the product of spherical tensor equivalent operators
AU - Sadovskii,D.A.
JF - Physics Letters A
JO - Phys.Lett.A
VL - 156
IS - 7-8
PY - 1991/07/01/
SP - 377
EP - 80
AB - A method is proposed to express a product of SO(3)-tensor equivalents in terms of an operator basis which comprises all the equivalents, both diagonal and nondiagonal in angular momentum, multiplied by powers of the number-of-spins scalar n=2j
KW - SO groups
KW - Other internal and higher symmetries in particle physics
ID - Sadovskii1991DS-tensor-prods
ER -
TY - JOUR
TI - Experimental study of a sequence of quantum bifurcations leading to the crossover of a rotational multiplet
AU - Davarashvili,O.I.
AU - Zhilinskii,B.I.
AU - Krivtsun,V.M.
AU - Sadovskii,D.A.
AU - Snegirev,E.P.
JF - JETP Letters
JO - JETP Lett.
J2 - Soviet JETP Lett.
N2 - in Russian (Pis'ma v Zh.Eksp.Theor.Phyz.) pp.17--19
VL - 51
IS - 1
PY - 1990/01/10/
SP - 18
EP - 21
AB - The `crossover' of the energy spectrum of a molecule during rotational excitation corresponds to a series of bifurcations in the classical limiting problem. The sequence and type of these bifurcations are determined by the symmetry conditions. This effect is studied in the high-resolution spectrum of R$_3$/sup -/band of the $\nu_3$ state of the CF$_4$ molecule
KW - molecular rotational vibrational structure
KW - spherical top molecules
KW - tetrahedral molecules
ID - Davarashvili1990DS-CF4-exp
ER -
TY - JOUR
TI - Manifestation of bifurcations and diabolic points in molecular energy spectra
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
AU - Champion,J.P.
AU - Pierre,G.
JF - Journal of Chemical Physics
JO - J.Chem.Phys.
VL - 92
IS - 3
PY - 1990/02/01/
SP - 1523
EP - 37
AB - The general scheme of the qualitative analysis of finite-particle quantum problems is discussed. Theoretical methods for the qualitative analysis of energy spectra in quantum problems are applied to the study of the rovibrational energy levels of spherical top molecules. The existence of modifications in the rotational cluster structure and of redistributions of the energy levels between different branches under the rotational excitation is shown for the $\nu_2$/ $\nu_4$ dyad of the /sup 12/CH$_4$ and /sup 28/SiH$_4$ molecules. An interpretation of the qualitative features of energy spectra in terms of bifurcations and formations of conical intersection points (diabolic points) on the energy surfaces of the corresponding classical problem is proposed
KW - molecular rotation vibration
KW - Vibrational rotational analysis molecular spectra
KW - Quantum theory
KW - spherical top molecules
ID - Sadovskii1990DS-manifestations
RP - IN FILE
L1 - /home/dima/public_html/preprints/JChemPhys_92_1523.djvu
ER -
TY - JOUR
TI - Critical phenomena and diabolic points in rovibrational energy spectra of spherical top molecules
AU - Krivtsun,V.M.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Journal of Molecular Spectroscopy
JO - J.Mol.Spectrosc.
VL - 139
IS - 1
PY - 1990/01//
SP - 126
EP - 46
AB - The qualitative modifications of the rovibrational energy-level structure under rotational excitation are studied for spherical top molecules. The $\nu_2$, $\nu_4$ bands of /sup 12/CD$_4$ and $^{120}$SnH$_4$ and the $\nu_1$, $\nu_3$ bands of $^{120}$SnH$_4$ are treated as examples. Two types of qualitative changes are shown to exist: the critical phenomena corresponding to the modification of the cluster structure and the so-called diabolic points associated with the redistribution of energy levels between different branches as the rotational quantum number increases. A simple model interpretation of energy-level redistribution is given to show that such a phenomenon is typical for tetrahedral molecules. Manifestation of critical phenomena and diabolic point formation in high-resolution infrared spectra are discussed
KW - critical phenomena
KW - molecular rotation vibration calculations
KW - organic compounds
KW - tin compounds
KW - Vibrational rotational analysis molecular spectra
ID - Krivtsun1990DS-SnH4-theor
ER -
TY - JOUR
TI - Diode laser study of the $\nu_1$ and $\nu_3$ bands of the $^{120}${SnH}$_4$ molecule
AU - Krivtsun,V.M.
AU - Sadovskii,D.A.
AU - Snegirev,E.P.
AU - Shotov,A.P.
AU - Zasavitskii,I.I.
JF - Journal of Molecular Spectroscopy
JO - J.Mol.Spectrosc.
VL - 139
IS - 1
PY - 1990/01//
SP - 107
EP - 25
AB - The absorption spectrum of the SnH$_4$ molecule has been measured with Doppler limited resolution in the region 1903-1960 cm$^{-1}$ by means of a tunable diode laser spectrometer. IR transitions of the Q and R branches of allowed $\nu_3$(F$_2$) and `forbidden' $\nu_1$(A$_1$) bands were observed. These two states were found to be strongly mixed by the rotational-vibrational interaction, and as a consequence of the $\nu_1$ band appears in absorption. Wavenumbers of transitions to the $\nu_1$, $\nu_3$ energy levels with the quantum number of angular momentum J=1-15 have been obtained with an accuracy of about 0.001 cm$^{-1}$. More than 230 transitions of the $^{120}$SnH$_4$ isotopic species were used for simultaneous analysis of the $\nu_1$, $\nu_3$ resonance states. In this way 21 spectroscopic parameters of the upper states have been determined using a model Hamiltonian which explicitly takes into account the resonance interaction. The parameters obtained reproduced the experimental spectrum with r.m.s. discrepancy of 0.002 cm$^{-1}$
KW - infrared spectra of polyatomic inorganic molecules
KW - molecular rotation vibration
KW - tin compounds
KW - tetrahedral molecules
KW - spherical top molecules
KW - Infrared molecular spectra
KW - Vibrational rotational analysis molecular spectra
ID - Krivtsun1990DS-SnH4-exp
ER -
TY - JOUR
TI - Qualitative changes in the structure of rovibrational levels. Dyad $\nu_2$, $\nu_4$ of spherical top molecules
AU - Zhilinskii,B.I.
AU - Sadovskii,D.A.
JF - Bulletin of the Academy of Sciences of the USSR, Physical Series
JO - Bull.Acad.Sci.USSR, Phys.Ser.
N2 - in Russian (Izvestiya Akademii Nauk SSSR, Seriya Fizika) pp.1736--1740
VL - 53
IS - 59
PY - 1989///
SP - 80
EP - 83
AB - For the example of the rotational structure of the dyad of interacting vibrational states $\nu_2$, $\nu_4$ of molecules of spherical-gyroscope type, theoretical analysis of the qualitative changes occurring in rotational excitation is undertaken
KW - molecular vibration rotations states
KW - Rovibrational interactions molecular spectra
KW - Rotational analysis molecular spectra
KW - tetrahedral molecules
KW - spherical top molecules
ID - Zhilinskii1989DS-40
ER -
TY - JOUR
TI - Contact transformations in tensor formalism. Effective Hamiltonian and dipole moment for the $\nu_2$, $\nu_4$ dyad of tetrahedral molecules
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Journal of Quantitative Spectroscopy and Radiative Transfer
JO - J.Quant.Spectr.Rad.Trans.
J2 - J.Q.S.R.T.
VL - 42
IS - 6
PY - 1989/12//
SP - 575
EP - 83
AB - Simultaneous unitary transformations of the effective Hamiltonian and the effective dipole moment are studied via an irreducible tensor formalism for the $\nu_2$, $\nu_4$ dyad of tetrahedral molecules. Large unitary transformations relating resonance and isolated band models are treated by taking into account the non-leading contributions and multiple commutators. The unitary equivalence of different parameter sets of the effective dipole moment is explicitly shown for the $\nu_2$, $\nu_4$ bands of /sup 12/CH$_4$
KW - spherical top molecules
KW - molecular vibration and rotations
KW - Vibrational and rotational analysis molecular spectra
KW - Molecular electric and magnetic moments and derivatives, polarizability, and magnetic susceptibility
ID - Sadovskii1989DS-ct-mu
ER -
TY - JOUR
TI - Organization of quantum bifurcations: crossover of rovibrational bands in spherical top molecules
AU - Pierre,G.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Europhysics Letters
JO - Europhys.Lett.
VL - 10
IS - 5
PY - 1989/11/01/
SP - 409
EP - 14
AB - Qualitative changes in the rotational structure of a finite particle quantum system are studied. The crossover phenomenon is explained from the point of view of consecutive quantum bifurcations. The generic organization of bifurcations is related to the stratification of the space of dynamical variables imposed by the invariance group of the Hamiltonian
KW - molecular rotation vibration calculations
KW - quantum theory
KW - Vibrational rotational analysis molecular spectra
KW - Algebraic methods in quantum theory
ID - Pierre1989DS-crossover-note
ER -
TY - JOUR
TI - Qualitative analysis of vibration-rotation Hamiltonians for spherical top molecules
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Molecular Physics
JO - Mol.Phys.
VL - 65
IS - 1
PY - 1988/09//
SP - 109
EP - 128
U1 - 10.1080/00268978800100891
AB - A new approach to the qualitative analysis of the rotational structure of a group of degenerate or quasidegenerate vibrational states is proposed. The approach is based on a quantum description of resonant vibrational states and on using classical methods when describing the rotational structure of these states. The approach is used for studying the rotational structure of two- and three-fold degenerate vibrational states of the tetrahedral AB$_4$ molecule as well as studying the $\nu_1$, $\nu_3$ diad of /sup 28/SiH$_4$. The general scheme of the analysis is realized by computer
KW - spherical top molecules
KW - Vibrational rotational analysis molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
KW - Rotational analysis molecular spectra
ID - Sadovskii1988DS-q-vibrot-MP
ER -
TY - JOUR
TI - On the dynamical meaning of the diabolic points
AU - Pavlov-Verevkin,V.B.
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Europhysics Letters
JO - Europhys.Lett.
VL - 6
IS - 7
PY - 1988/08/01/
SP - 573
EP - 8
U1 - 10.1209/0295-5075/6/7/001
AB - Using a simple exactly soluble quantum model, it is shown that the diabolic points may be associated with the qualitative phenomenon of the redistribution of the energy levels between different branches in the energy spectra
KW - Quantum theory
KW - spherical top molecules
ID - Pavlov-Verevkin1988DS-dp-note
ER -
TY - JOUR
TI - Qualitative changes in the rotational structure of vibrational states with increasing angular momentum
AU - Zhilinskii,B.I.
AU - Sadovskii,D.A.
JF - Optics and Spectroscopy
VL - 61
IS - 3
PY - 1986/09//
SP - 301
EP - 304
AB - The article proposes an effective method for describing the qualitative characteristics of the rotational structure of a group of vibrational states, based on a study of the stationary points of a system of classical surfaces of rotational energy. A scheme for constructing the energy surfaces for effective Hamiltonians with known spectroscopic parameters is described. The rotational structure is analyzed by means of energy diagrams showing the dependence of the stationary points on the rotational quantum number. The general scheme of the analysis was realized with a computer. An effective rotational Hamiltonian for the doubly degenerate vibrational state of methane is investigated as a specific example
N2 - in Russian (Optika i Spektroskopiya), pp.481--486
KW - spherical top
KW - tetrahedral molecules
KW - molecular rotation vibration
KW - rotational vibrational analysis molecular spectra
ID - Zhilinskii1986DS-q-vibrot-OS
ER -
TY - JOUR
TI - Invariant combinations of spectroscopic parameters of tetrahedral molecules
AU - Zhilinskii,B.I.
AU - Sadovskii,D.A.
JF - Moscow University Bulletin - Chemistry
JO - Moscow Univ.Bull.
VL - 27
SP - 145
EP - 148
PY - 1986///
N2 - in Russian (Vestnik Moskovskogo Universiteta, Khimiya)
KW - spherical top
KW - tetrahedral molecules
KW - molecular rotation vibration constants
ID - Zhilinskii1986DS-nu1nu3-Vestnik
ER -
TY - JOUR
TI - Theoretical analysis of spectroscopic constants for spherical tops: $\nu_2$, $\nu_4$ bands of {AB}$_4$ molecules
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Journal of Molecular Spectroscopy
JO - J.Mol.Spectrosc.
VL - 115
IS - 2
PY - 1986/02//
SP - 235
EP - 257
AB - Extended analysis of the different sets of spectroscopic constants for $\nu_2$, $\nu_4$ bands of CH$_4$, CD$_4$, SiH$_4$ is performed taking into account the possibility of the unitary transformation of the corresponding effective Hamiltonian. Refined relations between different notations of tensor operators and spectroscopic constants are presented. The unitary equivalence between several different sets of constants is shown up to the lambda /sup 4/ order
KW - spherical top
KW - tetrahedral molecules
KW - isotope effects
KW - molecular rotation vibration constants
KW - rotational vibrational analysis molecular spectra
ID - Sadovskii1986DS-nu2nu4
ER -
TY - JOUR
TI - Comparative analysis of spectroscopic constants of tetrahedral molecules: $\nu_1$ and $\nu_3$ bands of silane and germane
AU - Sadovskii,D.A.
AU - Zhilinskii,B.I.
JF - Optics and Spectroscopy
JO - Opt. \& Spectrosc.
VL - 58
IS - 3
PY - 1985/03//
SP - 344
EP - 347
AB - Explicit transformation formulas are obtained for reduction of the model effective Hamiltonian used to describe the vibrational quasi-degenerate $\nu_1$ and $\nu_3$ states in molecules with tetrahedral symmetry. Using the example of SiH$_4$ and /sup 74/GeH$_4$ molecules, employing a reduction transformation, a comparative analysis of processing performed by various authors is conducted, and the stability of spectroscopic parameters is investigated on a change to reduced-model effective Hamiltonians
N2 - in Russian (Optika i Spektroskopiya) pp.565--570, in English pp.490--492
KW - spherical top molecules
KW - germanium compounds
KW - silicon compounds
KW - molecular rotation and vibration
KW - rotational vibrational analysis molecular spectra
KW - Molecular rotation, vibration, and vibration rotation constants
ID - Sadovskii1985DS-nu1nu3
ER -