Equipartition of energy in a one-dimensional model of diatomic molecules. II. Maximal Lyapunov exponent and phase-space trajectory separation

Journal Article · Fri Feb 15 00:00:00 EST 1991 · Physical Review, A; (USA)

DOI:https://doi.org/10.1103/PhysRevA.43.2031· OSTI ID:5838137

Monge, A; Cohen, E G.D. ^[1]; Erpenbeck, J J ^[2]

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1. The Rockefeller University, New York, New York 10021 (US)
2. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (USA)

The Lyapunov instability is studied numerically for a one-dimensional model of diatomic molecules with harmonic intramolecular and hard intermolecular interactions. Previous results are extended to characterize the equipartition regime in terms of the two parameters of the system, the number of molecules {ital n} and the vibrational frequency {omega}. When the system is in equipartition, we find the existence of a thermodynamic limit for the maximal Lyapunov exponent and a power-law behavior {omega}{sup {alpha}}, in analogy with the Fermi-Pasta-Ulam model. The separation of trajectories in phase space, investigated by considering the time dependence of the distance of initially close trajectories and by averaging over the phase space, is related to the maximal Lyapunov exponent and shown to be an alternative way to compute it when {ital n} is not too large. Multiple-precision arithmetic analysis for the model and its link to Lyapunov instability are also discussed.

• DOE Contract Number: FG02-88ER13847
• OSTI ID: 5838137
• Journal Information: Physical Review, A; (USA), Vol. 43:4; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
MOLECULAR MODELS
PHASE SPACE
DEGREES OF FREEDOM
ENERGY SPECTRA
LYAPUNOV METHOD
ONE-DIMENSIONAL CALCULATIONS
OSCILLATION MODES
TWO-BODY PROBLEM
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MATHEMATICAL SPACE
SPACE
SPECTRA
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory