Decay of the classical Loschmidt echo in integrable systems

2003/04/16 by Giuliano Benenti, Giulio Casati, Gregor Veble · 3 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #cond-mat #nlin.CD #nlin.SI

paper · pdf · doi:10.1103/physreve.68.036212

published as Phys. Rev. E 68, 036212 (2003) · 8 pages, 3 figures, revtex

arxiv created 2003/04/16 · openalex publication_date 2003/09/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study both analytically and numerically the decay of fidelity of classical motion for integrable systems. We find that the decay can exhibit two qualitatively different behaviors, namely, an algebraic decay that is due to the perturbation of the shape of the tori or a ballistic decay that is associated with perturbing the frequencies of the tori. The type of decay depends on initial conditions and on the shape of the perturbation but, for small enough perturbations, not on its size. We demonstrate numerically this general behavior for the cases of the twist map, the rectangular billiard, and the kicked rotor in the almost integrable regime.

Citations

• Stability of classical chaotic motion under a system’s perturbations

Cited by

• Classical versus quantum errors in quantum computation of dynamical systems
• The Loschmidt echo in classically chaotic systems: Quantum chaos, irreversibility and decoherence
• The quantum fidelity for the time-periodic singular harmonic oscillator

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