Quantum-classical correspondence in perturbed chaotic systems

2001/12/10 by Giuliano Benenti, Giulio Casati · 6 citations
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Scientific Research and Discoveries #cond-mat #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.65.066205

published as Phys. Rev. E 65, 066205 (2002) · revtex, 5 pages, 5 figures

arxiv created 2001/12/10 · openalex publication_date 2002/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the behavior of fidelity for a classically chaotic quantum system. We show the existence of a critical value of the perturbation above which the quantum decay, exponential or power law, follows the classical one. The independence of the decay rate of the perturbation strength, discussed in the literature, is a consequence of the quantum-classical correspondence of the relaxation process.

Citations

• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

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
• Energy dissipation via coupling with a finite chaotic environment
• Signatures of Quantum Stability in a Classically Chaotic System
• Universality of the Lyapunov regime for the Loschmidt echo

Related

• Stability of classical chaotic motion under a system’s perturbations
• Stability of Quantum Dynamics
• Quantum Chaos and Quantum-Classical Correspondence
• Classical versus quantum errors in quantum computation of dynamical systems
• Stabilizing quantum dynamics through coupling to a quantized environment