Classical Loschmidt echo in chaotic many-body systems

Abstract

General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations which 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 whether the initial phase-space density is continuous or not.

4 RevTeX pages, 4 figures

References in corpus (5)

• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Stability of quantum motion and correlation decay
• Faster than Lyapunov decays of classical Loshcmidt echo
• Echoes in classical dynamical systems
• On the stability of classical chaotic motion under system's perturbations

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• Asymptotic Prethermalization in Periodically Driven Classical Spin Chains
• Chaos and Complexity of quantum motion
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Quantum echo dynamics in the Sherrington-Kirkpatrick model
• Beating the efficiency of both quantum and classical simulations with semiclassics
• Breaking the exponential wall in classical simulations of fidelity