Largest Lyapunov Exponent for Many Particle Systems at Low Densities

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.