Anomalous power law of quantum reversibility for classically regular dynamics

Abstract

The Loschmidt Echo M(t) (defined as the squared overlap of wave packets evolving with two slightly different Hamiltonians) is a measure of quantum reversibility. We investigate its behavior for classically quasi-integrable systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2 depending solely on the dimension d of the system. This power law decay is faster than the result ~ t^{-d} for the decay of classical phase space densities.

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• Universality of the Lyapunov regime for the Loschmidt echo
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• Dephasing representation of quantum fidelity for general pure and mixed states
• Quantum freeze of fidelity decay for a class of integrable dynamics
• Quantum Fidelity Decay of Quasi-Integrable Systems
• Recurrence of fidelity in near integrable systems
• Decay of the classical Loschmidt echo in integrable systems
• Algebraic fidelity decay for local perturbations
• Probing Localization in Absorbing Systems via Loschmidt Echos
• Critical Fidelity
• Quantum Reversibility: Is there an Echo?
• Stability of quantum motion in regular systems: a uniform semiclassical approach
• Loschmidt echo for a chaotic oscillator
• Mesoscopic Fluctuations of the Loschmidt Echo
• Engineering fidelity echoes in Bose-Hubbard Hamiltonians
• Decay of the Loschmidt echo in a time-dependent environment
• Semiclassical Approach to Survival Probability at Quantum Phase Transitions
• The Effects of Symmetries on Quantum Fidelity Decay
• The quantum fidelity for the time-dependent singular quantum oscillator
• About Quantum Revivals, Quantum Fidelity, A semiclassical Approach
• On the origin of the exponential decay of the Loschmidt echo in integrable systems
• A unified time scale for quantum chaotic regimes
• Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart
• Sensitivity of Quantum Motion to Perturbation in Triangle Map
• Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown
• Short-Time Loschmidt Gap in Dynamical Systems with Critical Chaos
• Out-of-Time-Order-Correlation in perturbed quantum wells