On the stability of classical chaotic motion under system's perturbations

Abstract

We study in detail the time behavior of classical fidelity for chaotic systems. We show in particular that the asymptotic decay, depending on system dynamical properties, can be either exponential, with a rate determined by the gap in the discretized Perron-Frobenius operator, or algebraic, with the same power as for correlation functions decay. Therefore the decay of fidelity is strictly connected to correlations decay.

4 pages, 5 figures, revtex; revised title, abstract and introduction, with minor modifications in the main text

References in corpus (13)

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• Long-Time Correlations in the Stochastic Regime
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
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• Stability of quantum motion and correlation decay
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• Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
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Cited by in corpus (23)

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• Loschmidt Echo
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Semiclassical evaluation of quantum fidelity
• Universality of the Lyapunov regime for the Loschmidt echo
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• How complex is the quantum motion?
• Universal Long-time Behavior of Nuclear Spin Decays in a Solid
• Quantum freeze of fidelity decay for a class of integrable dynamics
• Faster than Lyapunov decays of classical Loshcmidt echo
• Uniform semiclassical approach to fidelity decay in the deep Lyapunov regime
• On the long-time behavior of spin echo and its relation to free induction decay
• Uniform Semiclassical Approach to Fidelity Decay: from Weak to Strong Perturbation
• Quantum Fidelity Decay of Quasi-Integrable Systems
• Decay of the classical Loschmidt echo in integrable systems
• Complexity of Quantum States and Reversibility of Quantum Motion
• Beating the efficiency of both quantum and classical simulations with semiclassics
• Classical Loschmidt echo in chaotic many-body systems
• Quantum dephasing and decay of classical correlation functions in chaotic systems
• About Quantum Revivals, Quantum Fidelity, A semiclassical Approach
• The quantum fidelity for the time-dependent singular quantum oscillator
• Quantum and Classical Fidelity for Singular Perturbations of the Inverted and Harmonic Oscillator
• Breaking the exponential wall in classical simulations of fidelity