Equipartition of energy in a one-dimensional model of diatomic molecules

Journal Article · Thu Sep 15 04:00:00 EDT 1988 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.38.3054· OSTI ID:7063070

Erpenbeck, J J; Cohen, E G.D.

A one-dimensional model of diatomic molecules with harmonic intramolecular forces and highly anharmonic (hard-rod) intermolecular forces is studied numerically. This interaction allows a numerical integration of the equations of motion with only rounding errors, but no truncation errors. The goal was to investigate the transition from dynamics to classical statistical mechanics for this model; in particular, to check deviations from equipartition and ergodicity which have been reported in the literature for similar models. For a given number of molecules and small vibrational frequencies (much lower than those which occur in nature), no equipartition is found. However, with increasing frequency, equipartition is established, first between the two vibrational degrees of freedom and then also with the translational motion of the molecules. While for a small number of molecules and small frequencies Kol'ogorov-Arnol'd-Moser--like motion dominates, this behavior changes with increasing frequency to chaotic motion. The decay time of the vibrational-energy--time correlation function does not show any increase with frequency, in contrast to what G. Benettin, L. Galgani, and A. Giorgilli (Phys. Lett. A 120, 23 (1987)) found for a model, similar to ours but with a soft repulsive interaction. Thus, the present model behaves in accordance with classical statistical mechanics.

• Research Organization: Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 7063070
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 38:6; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENERGY LEVELS
ENERGY SPECTRA
EXCITED STATES
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MECHANICS
MOLECULAR MODELS
OSCILLATION MODES
ROTATIONAL STATES
SPECTRA
STATISTICAL MECHANICS
TWO-BODY PROBLEM
VIBRATIONAL STATES