Publications and presentations

Monodromy in atoms and molecules

• K. Efstathiou, D. A. Sadovskií, & B. I. Zhilinskií, Classification of perturbations of the hydrogen atom by small static electric and magnetic fields, Proc. Roy. Soc. A in press.
• Michaël Sanrey, M. Joyeux, & D. A. Sadovskií, Classical and quantum-mechanical plane switching in CO₂, J. Chem. Phys. 124 074318 (2006), 12 pages; abstract, pdf (882 kB)
• Richard H. Cushman, Holger R. Dullin, Andrea Giacobbe, Darryl D. Holm, Marc Joyeux, Peter Lynch, D. A. Sadovskií, & Boris I. Zhilinskií, CO₂ molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy, Phys. Rev. Lett. 93(2) 024302 (2004). abstract, pdf 250k
• Marc Joyeux, D. A. Sadovskií, & J. Tennyson, Monodromy of the LiNC/NCLi molecule,
  Chem. Phys. Lett. 382(3-4), 439-442 (2003). abstract
• K. Efstathiou, Marc Joyeux, & D. A. Sadovskií, Global bending quantum number and the absence of monodromy in the HCN↔CNH molecule,
  Phys. Rev. A 69(3), 032504-1--15 (2004). abstract
• R. H. Cushman & D. A. Sadovskií, Monodromy in perturbed Kepler systems: hydrogen atom in crossed fields,
  Europhysics Letters 47(1), 1-7 (1999). abstract
• R. H. Cushman & D. A. Sadovskií, Monodromy in the hydrogen atom in crossed fields,
  Physica D 142 166-96 (2000). abstract pdf (858 kB)

  Theory of quantum and classical monodromy

• D. A. Sadovskií & B. I. Zhilinskií, Hamiltonian systems with detuned 1:1:2 resonance: Manifestation of bidromy, Annals Phys. 322(1), 164-200 (January Special Issue 2007).
• N. N. Nekhoroshev, D. A. Sadovskií & B. I. Zhilinskií, Fractional Hamiltonian monodromy, Annales Henri Poincaré, 7 1099--1211 (2006).
• K. Efstathiou, R. H. Cushman, & D. A. Sadovskií, Fractional monodromy of the 1:(-2) resonance, Adv. in Math. 209(1) 241--273 (2007); online 12 July 2006;
• D. A. Sadovskií & B. I. Zhilinskií, Quantum monodromy, its generalizations and molecular manifestations, Mol. Phys. 104(16--17) 2595--2615 (2006).
  Short popular review of recent developments of monodromy including bidromy and applications in molecular spectra; a followup to the poster presented by B. I. Zhilinskií at the 19^th International Colloquium on High Resolution Spectroscopy in Salamanca, Spain, 2005.
• A. Giacobbe, R. H. Cushman, D. A. Sadovskií, & B. I. Zhilinskií, Monodromy of the quantum 1:1:2 resonant swing spring, J. Math. Physics, 45(12) 5076--100 (2004).
• Nikolaí N. Nekhoroshev, D. A. Sadovskií & Boris I. Zhilinskií, Fractional monodromy of resonant classical and quantum oscillators (Monodromie fractionnaire des oscillateurs résonnants),
  Comptes Rendus Acad. Sci. Paris, Ser. I 335, 985--88 (2002). abstract
• No Polar Coordinates. Lectures by Richard Cushman, Presented at the first MASIE summer school held in Peyresq, Alpes du Sud, France 2-16 September 2000. Text prepared by Konstantinos Efstathiou & D. A. Sadovskií (coordinating editor); final revision February 3, 2003.
  R.C. declines to take any responsibility for the contents of these notes even though he helped write and typeset them, contributed his scratchy notes to the preparers, and wrote up his homework.
  Published in Geometric Mechanics and Symmetry. The Peyresq Lectures, Edited by James Montaldi & Tudor Ratiu, London Mathematical Society Lecture Note Series No. 306 (Cambridge University Press, Cambridge UK, June 2005) 412 pages; ISBN: 9780521539579 - see frontmatter
• D. A. Sadovskií & Boris I. Zhilinskií, Monodromy, diabolic points, and angular momentum coupling,
  Physics Letters 256(4), 235--44 (1999). abstract
• Lucien Grondin, D. A. Sadovskií & Boris I. Zhilinskií, Monodromy as topological obstruction to global action-angle variables in systems with coupled angular momenta and rearrangement of bands in quantum spectra, Phys. Rev. A 65 012105-1--15 (Dec. 2001) abstract

  Normal forms, Relative equilibria

• Igor N. Kozin, D. A. Sadovskií, & B. I. Zhilinskií, Assigning vibrational polyads using relative equilibria: application to ozone, Spectrochim. Acta A, 61(13-14) 2867-2885 (2005)
• Konstantinos Efstathiou & D. A. Sadovskií, Perturbations of the 1:1:1 resonance with tetrahedral symmetry: a three degree of freedom analogue of the two degree of freedom Hénon-Heiles Hamiltonian,
  Nonlinearity 17 415-446 (2004). abstract,
• K. Efstathiou, R. H. Cushman, & D. A. Sadovskií, Linear Hamiltonian Hopf bifurcation for point group invariant perturbations of the 1:1:1 resonance,
  Proc. Roy. Soc. Lond. Ser. A 459 2997--3019 (2003).
• K. Efstathiou, D. A. Sadovskií, & B. I. Zhilinskií, Analysis of rotation-vibration relative equilibria on the example of a tetrahedral four atom molecule,
  SIADS (SIAM Journal of Applied Dynamical Systems) 3(3) 261-351 (2004). abstract,
• D. A. Sadovskií, Normal forms, geometry, and dynamics of atomic and molecular systems with symmetry, in Symmetry and Perturbation Theory (Proceedings of the international conference SPT2001), D. Bambusi, M. Cadoni, & G. Gaeta editors, ISBN 981-02-4793-1 (World Scientific, Singapore, 2001), pp. 191-205. Errata: the Hénon-Heiles Hamiltonian got wrong, eq. (1) should read: Presented at the special session dedicated to the memory of Louis Michel, Cala Gonone, Sardinia, May 11, 2001.
• Christophe Van Hecke, D. A. Sadovskií, B. I. Zhilinskií, & V. Boudon, Rotational-vibrational relative equilibria and the structure of quantum energy spectrum of the tetrahedral molecule P₄, European Phys. J. D17, 13-35 (2001). abstract
• Ch. Van Hecke, D. A. Sadovskií, & B. I. Zhilinskií,
  Qualitative analysis of molecular rotation starting from inter-nuclear potential, European Phys. J. D7, 199-209 (1999). abstract
• D. A. Sadovskií, N. G. Fulton, J. R. Henderson, J. Tennyson, & B. I. Zhilinskií, Nonlinear normal modes and local bending vibrations of H₃⁺ and D₃⁺, J. Chem. Phys. 99(2), 906-18 (1993).

  Perturbed Kepler problem(H atom in fields)

• K. Efstathiou, R. H. Cushman & D. A. Sadovskií, Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields, Physica D, 194, 250-274 (2004).
• Richard H. Cushman & D. A. Sadovskií, Monodromy in the hydrogen atom in crossed fields, Physica D 142 166-96 (2000); Monodromy in perturbed Kepler systems: hydrogen atom in crossed fields, Europhysics Letters 47(1), 1-7 (1999). abstract
• D. A. Sadovskií & Boris I. Zhilinskií, Tuning the hydrogen atom in crossed fields between the Zeeman and Stark limits, Phys. Rev. A 57(4), 2867-84 (1998). abstract
• D. A. Sadovskií, Boris I. Zhilinskií & Louis Michel, Collapse of the Zeeman structure of the hydrogen atom in the external electric field, preprint IHES P/95/86, Bures-sur-Yvette, 1995; Phys. Rev. A 53(6) 4064-7 (1996) pdf.

  Normal form study of bifurcations of periodic orbits

• D. A. Sadovskií & John B. Delos, Bifurcation of periodic orbits of Hamiltonian systems: Analysis using normal form theory, Phys. Rev. E 54(2) 2033-70 (1996); Organization of bifurcations of periodic orbits, Phys. Rev. Lett. 75(11), 2120--3 (1995).

  Qualitative theory of quantum systems

• D. A. Sadovskií & B. I. Zhilinskií, Counting levels within vibrational polyads. Generating function approach, J. Chem. Phys. 103(24), 10520--36 (1995).
• D. A. Sadovskií & B. I. Zhilinskií, Qualitative study of a model three level Hamiltonian with SU(3) dynamical symmetry, Phys. Rev. A 48(2), 1035-44 (1993).
  Group theoretical and topological analysis of localized vibration-rotation states, Phys. Rev. A 47(4), 2653-71 (1993).
• Victor E. Pavlov-Verevkin, D. A. Sadovskií & B. I. Zhilinskií, On the dynamical meaning of diabolic points, Europhys. Lett. 6, 573-78 (1988).
• Vl. M. Krivtsun, D. A. Sadovskií & B. I. Zhilinskií, Critical Phenomena and Diabolic Points in Rovibrational Energy Spectra of Spherical Top Molecules, J. Molec. Spectr. 139, 126-46 (1990).
• D. A. Sadovskií, Boris I. Zhilinskií, Jean-Paul Champion & Gérard Pierre, Manifestations of bifurcations and diabolic points in molecular energy spectra, J. Chem. Phys. 92, 1523-37 (1990).
• D. A. Sadovskií & Boris I. Zhilinskií, Qualitative analysis of vibration-rotation Hamiltonians for spherical top molecules, Molec. Phys. 65, 109-28 (1988).

  Rotation-vibration analysis of spherical top molecules

• Guillaume Dhont, D. A. Sadovskií, B. I. Zhilinskií, & Vincent Boudon, Analysis of the “unusual” vibrational components of triply degenerate vibrational mode ν₆ of Mo(CO)₆ based on the classical interpretation of the effective rotation-vibration Hamiltonian, J. Mol. Spectrosc. 201, 95-108 (2000).
• D. A. Sadovskií, Standard decomposition of the products of spherical tensor equivalent operators, Phys. Lett. A 156, 377-80 (1991).
• Vl. M. Krivtsun, D. A. Sadovskií, E. P. Snegirev, A. P. Shotov, & I. I. Zasavitskií, Diode laser study of the ν₁ and ν₃ bands of the ¹²⁰SnH₄ molecule, J. Mol. Spectrosc. 139, 107-25 (1990).
• Gérard Pierre, D. A. Sadovskií & B. I. Zhilinskií,
  Organization of quantum bifurcations: Crossover of rovibrational bands in spherical top molecules,
  Europhys. Lett. 10, 409-14 (1989).
• Victor E. Pavlov-Verevkin, D. A. Sadovskií & B. I. Zhilinskií,
  On the dynamical meaning of diabolic points, Europhys. Lett. 6, 573-78 (1988).
• D. A. Sadovskií & Boris I. Zhilinskií,
  Qualitative analysis of vibration-rotation Hamiltonians for spherical top molecules, Molec. Phys. 65, 109-28 (1988).
• D. A. Sadovskií & Boris I. Zhilinskií,
  Contact transformations in tensor formalism. Effective Hamiltonian and dipole moment for the ν₂ , ν₄ dyad of tetrahedral molecules, J. Qualitat. Spectrosc. Radiat. Transf. 42, 575-84 (1989).
• D. A. Sadovskií & Boris I. Zhilinskií, Theoretical analysis of spectroscopic constants for spherical tops: ν₂ , ν₄ bands of AB₄ molecules, J. Mol. Spectrosc. 115, 235-57 (1986).
• B. I. Zhilinskií & D. A. Sadovskií, Comparative study of spectroscopic constants of tetrahedral molecules: ν₁ , ν₃ bands of silane and germane, Opt. Spectrosc. (USSR) 58, 565-70 (1985).

Rydberg diatomic molecules

• Izabel Dabrowski & D. A. Sadovskií, Spectra of rare gas hydrides. VI. nf Rydberg complex of KrD,
  J. Chem. Phys. 107(21), 8874-85 (1997).
• I. Dabrowski & D. A. Sadovskií, Spectra of rare gas hydrides. V: np Rydberg series of KrD,
  Molec. Physics 81(2), 291-326 (1994).
• I. Dabrowski, Gerhard Herzberg, John W.C. Johns, D. A. Sadovskií, & M. Vervloet, Spectra of rare gas hydrides. IV. Three new bands of argon deuteride involving a low-lying ``p'' Rydberg state of ArD,
  J. Chem. Phys. 97, 7093-111 (1992).

  Theses

• présentation de la thèse d'habilitation à diriger des recherches (HDR),
  Etude dynamique de systèmes quantiques [en français, 70 p], titre, sommaire et résumé de la thèse HDR
  Dynamical study of quantum systems [in English, 70 p], title, contents, and abstract of the HDR thesis
  soutenue à l'Université du Littoral, Dunkerque, le 19 juin 1998
• Rovibrational spectra and structure of quasidegenerate vibrational states of spherical top molecules, Ph.D. thesis in physics, specialization “Optics”, Institute of Spectroscopy (ISAN), USSR Academy of Sciences, Troitzk, Moscow Region, 1989 [in Russian]
• Analysis of model effective Hamiltonians of tetrahedral molecules, masters thesis in chemistry, Moscow State University, 1984 [in Russian]

  Presentations

• Monodromie quantique et ses applications (373K), French version of a poster used together with Boris Zhilinskií in several presentations during 2005.
• Manifestation of monodromy in molecular energy level spectra examples of HCN/CNH vs LiNC/NCLi and CO₂, Journées semi-classiques moléculaires organized by San Vu Ngoc, Institut Fourier, Grenoble, 2-4 février, 2004
• Quantum and classical monodromy. Geometric analysis of perturbed hydrogen atom and similar systems, poster. Gordon Conference on Atomic Physics, New Hampshire, 4-9 July (1999)
• Equilibres relatifs de systèmes moléculaires réels, Séminaire presenté au Laboratoire de Physique Université de Bourgogne (Dijon) et Laboratoire de Spectrométrie Physique Université Joseph Fourier (Grenoble I) le 27 et 29 novembre 2001
• Derivation of Nonlinear Normal Modes from the Reduced Problem, Workshop on Nonlinear Dynamics and Spectra, organized by Mark Roberts, Mathematics Institute, Warwick, UK, March 18-21, 1997