GEOMETRIC DYNAMICAL OBSERVABLES IN RARE-GAS CRYSTALS

We present a detailed description of how a differential geometric appr oach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic sys tem, a model of a rare gas solid. Such a geometric approach allows us to locate the energy threshold between weakly and strongly chaotic reg imes, and to estimate the largest Lyapunov exponent; We show how stand ard methods of classical statistical mechanics, i.e., Monte Carlo simu lations, can be used for our computational purposes. Finally we consid er a Lennard-Jones crystal modeling solid xenon. The value of the ener gy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to e quilibrium obtained in a previous work by molecular dynamics simulatio ns.