Loschmidt Echo and the Local Density of States

Abstract

Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpected non-uniform decay rate as a function of the perturbation strength instead of that Lyapunov decay. Here we study the systematic behavior of this regime in perturbed cat maps. We show that some perturbations produce coherent oscillations in the width of LDOS that imprint clear signals of the perturbation in LE decay. We also show that if the perturbation acts in a small region of phase space (local perturbation) the effect is magnified and the decay is given by the width of the LDOS.

8 pages, 8 figures

References in corpus (3)

• Dynamics of Loschmidt echoes and fidelity decay
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Long-time saturation of the Loschmidt echo in quantum chaotic billiards

Cited by in corpus (22)

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• Leaking Chaotic Systems
• Quench Dynamics of Isolated Many-Body Quantum Systems
• General Features of the Relaxation Dynamics of Interacting Quantum Systems
• Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra
• Beating the efficiency of both quantum and classical simulations with semiclassics
• Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
• Universal Response of Quantum Systems with Chaotic Dynamics
• Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor
• Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system
• Path integral approach to the quantum fidelity amplitude
• Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents
• Quantum information scrambling in two-dimensional Bose-Hubbard lattices
• Discrepancies between decoherence and the Loschmidt echo
• Semiclassical approach to fidelity amplitude
• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Non-monotonous short-time decay of the Loschmidt echo in quasi-one-dimensional systems
• Lyapunov decay in quantum irreversibility
• Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown
• Perturbations and chaos in quantum maps
• Exponential distillation of dominant eigenproperties
• Irreversibility in quantum maps with decoherence