Geometric dynamical observables in rare gas crystals

Details Geometric dynamical observables in rare gas crystals Geometric dynamical observables in rare gas crystals

1996-11-20

arxiv.org/abs/chao-dyn/9611010v1

Physical Review E 55, 2539 (1997)

Nonlinear Sciences

Chaotic Dynamics

RevTeX, 19 pages, 6 PostScript figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.55.2539

We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard mehods of classical statistical mechanics, i.e. Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The value of the energy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to equilibrium obtained in a previous work by molecular dynamics simulations.

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