Largest Lyapunov Exponent for Many Particle Systems at Low Densities

Details Largest Lyapunov Exponent for Many Particle Systems at Low Densities Largest Lyapunov Exponent for Many Particle Systems at Low Densities

1997-10-27

arxiv.org/abs/chao-dyn/9710020v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, RevTeX, 2 Figures (encapsulated postscript). Submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.80.2035

The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.

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