Echoes in classical dynamical systems

Abstract

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.

to be published in J. Phys. A

Cited by in corpus (24)

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• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• Anomalous power law of quantum reversibility for classically regular dynamics
• Quantum freeze of fidelity decay for a class of integrable dynamics
• Faster than Lyapunov decays of classical Loshcmidt echo
• On the stability of classical chaotic motion under system's perturbations
• Quantum Fidelity Decay of Quasi-Integrable Systems
• Decay of the classical Loschmidt echo in integrable systems
• Loschmidt echo for a chaotic oscillator
• Classical Loschmidt echo in chaotic many-body systems
• Stability of wave packet dynamics under perturbations
• Quantum dephasing and decay of classical correlation functions in chaotic systems
• The survival probability and the local density of states for one-dimensional Hamiltonian systems
• The quantum fidelity for the time-dependent singular quantum oscillator
• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Order-disorder transitions in a sheared many body system
• Towards a quantum time mirror for nonrelativistic wave packets
• Quantum and Classical Fidelity for Singular Perturbations of the Inverted and Harmonic Oscillator
• Breaking the exponential wall in classical simulations of fidelity