Dynamics of a Diatomic Molecule in a Trap
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MOLECULES, OPTICS
Dynamics of a Diatomic Molecule in a Trap N. N. Rosanova,b,c,* and N. V. Vysotinaa a Vavilov
b
State Optical Institute, St. Petersburg, 199053 Russia St. Petersburg National Research University of Information Technologies, Mechanics, and Optics “ITMO University,” St. Petersburg, 197101 Russia c Ioffe Physical–Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia *e-mail: [email protected] Received December 28, 2018; revised January 27, 2019; accepted January 29, 2019
Abstract—The dynamics of a diatomic molecule possessing translational, rotational, and vibrational degrees of freedom in a trap has been analyzed theoretically and numerically. The interaction of atoms in the molecule is described by the Lennard-Jones potential, while the interaction of atoms with the trap walls is described by an exponential potential of repulsion. The motion of a molecule away from the trap walls can be reduced to the classical two-body problem with the central interaction and is regular. It has been established that an intense interaction of atoms of the molecule with the trap walls leads to stochastization of motion. DOI: 10.1134/S1063776119060074
1. INTRODUCTION Analysis of the Ulam problem [2] concerning the dynamics of a classical particle in a trap with oscillating walls and related to the Fermi problem [1] played an important role in refining the fundamentals of statistical physics and in the development of the dynamic chaos theory with various applications [3–6]. These publications contain the results of direct numerical simulation as well as analytic results including those obtained using an approximate approach based of diffusion equations [6]. Nevertheless, this field also involves new problems including the replacement of a point particle by a more complex object with an internal structure and additional degrees of freedom. In [7], the motion of a soliton of the Bose–Einstein condensate with a spatial distribution between oscillating walls was investigated. At the same time, it is natural to consider a simpler object, viz., a system of two interacting classical particles simulating a diatomic molecule, which is the object of our investigation. The classical description of the motion of nuclei of a molecule [8] is well known and is justified in view of considerable mass of the nuclei as compared to the electron mass. Quantum effects must be taken into account mainly at extremely low vibrational energies comparable with the energy of a vibrational quantum; however, this energy range is not considered in this article. It appears that the study of spectroscopy and internal motion of isolated molecules has become important in connection with advances in the development of traps and methods of cooling of such objects [9–13],
as well as the possibility to observe intrinsic molecular motion using extremely short (attosecond) pulses [14–17]. The presence of relative vibrations about the equilibrium position, which is inherent in two- and many-particle systems, is of special interest
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