Equipartition of energy in a one-dimensional model of diatomic molecules. III. Soft-interaction case
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (USA)
- The Rockefeller University, New York, New York 10021 (USA)
The model of a one-dimensional, diatomic gas with harmonic intramolecular forces and soft intermolecular forces, introduced by Benettin, Galgani, and Giorgilli (Phys. Lett. A 120, 23 (1987)), is studied numerically for a set of initial conditions for various values of the vibrational frequency {omega} and the number of molecules {ital N}. The use of many trajectories, rather than a single one, as was done before, allows us to infer conclusions about the structure of the phase space of the system using statistical analysis of simple functions of the phase. Thus, for fixed {omega} and small {ital N}, the average vibrational energy differs from trajectory to trajectory, implying nonergodic behavior. However, these differences become statistically insignificant for large {ital N}, implying a transition to ergodicity. While this transition is not sharp, it occurs at larger {ital N} for increasing {omega}, due to the increasingly difficult exchange of energy between vibrational and translational degrees of freedom. The phase-space-averaged vibrational-energy time-autocorrelation function decays on two time scales for all frequencies considered, at least for {ital N} large enough that the system behaves ergodically. A rapid, Gaussian decay on the time scale of the mean free time is followed by a much slower, approximately stretched-exponential decay, due to interactions with adiabatic islands in phase space. This second time scale increases sharply with {omega} and is related to the increasingly slow, possibly Arnold-like, diffusion in phase space.
- DOE Contract Number:
- FG02-88ER13847
- OSTI ID:
- 5461433
- Journal Information:
- Physical Review, A; (USA), Vol. 43:10; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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