Lyapunov decay in quantum irreversibility

Abstract

The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is done. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as it was shown for quantum maps. In this work we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime.

8 pages, 6 figures. Accepted in Phil. Trans. R. Soc. A

References in corpus (8)

• Dynamics of Loschmidt echoes and fidelity decay
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Loschmidt Echo
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Purity and State Fidelity of Quantum Channels via Hamiltonians
• Dephasing representation of quantum fidelity for general pure and mixed states
• Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents
• Relaxation of isolated quantum systems beyond chaos

Cited by in corpus (3)

• Quantum to classical transition in the work distribution for chaotic systems
• Out-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?
• Periodicity of dynamical signatures of chaos in quantum kicked top