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DY: Dynamik und Statistische Physik

DY 40: Lyapunov Instability of Many-Body Systems

DY 40.1: Hauptvortrag

Donnerstag, 11. März 2004, 09:30–10:00, H2

Lyapunov instability of many-body systems — •Harald A. Posch — Institute for Experimental Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria

The evolution of classical many-body systems is highly unstable with respect to (infinitesimal) perturbations of phase-space states. Such perturbations grow, or shrink, exponentially with time. This is described by a set of rate constants, the Lyapunov spectrum. We demonstrate that in thermodynamic equilibrium the perturbations associated with the slowest growth rates are coherently spread out in space, reminiscent of the modes of fluctuating continuum mechanics. The “Lyapunov modes” display a linear dispersion relation for small wave numbers, which allows to construct the relevant part of the Lyapunov spectrum for systems close to the thermodynamic limit. For dynamically- thermostated systems in stationary nonequilibrium states the phase-space probability distribution is a fractal set with a dimension smaller than the dimension of phase space. This reduction in dimensionality is computed from the Lyapunov spectrum. It is shown to be an extensive quantity and may, by far, exceed the dimensions contributed by the thermostated degrees of freedom. The fractal nature of phase space is a fingerprint of the second law of thermodynamics and is the consequence of a constant rate of entropy production.