Classical Loschmidt echo in chaotic many-body systems.

General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations that affect essentially all degrees of freedom we find a doubly exponential decay with the rate determined by the largest Lyapunov exponent. The scaling of the decay rate on the perturbation strength depends on the continuity properties of the initial phase-space density.