Discrepancies between decoherence and the Loschmidt echo

Abstract

The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the loss of coherence produced by an environment coupled to the system. For classically chaotic systems both quantities display a number of -- supposedly universal -- regimes that can lead on to think of them as equivalent quantities. We study the decay of the Loschmidt echo and the purity for systems with finite dimensional Hilbert space and present numerical evidence of some fundamental differences between them.

6 pages, 3 figures. Changed title. Added 1 figure. Published version.

References in corpus (8)

• Dynamics of Loschmidt echoes and fidelity decay
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator
• Nonexponential decoherence and momentum subdiffusion in a quantum Lévy kicked rotator
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• Loschmidt Echo and the Local Density of States
• Entanglement-screening by nonlinear resonances
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Cited by in corpus (6)

• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
• Lyapunov Decoherence Rate in Classically Chaotic Systems
• The importance of level statistics for the decoherence of a central spin due to a spin environment
• Semiclassical approach to fidelity amplitude
• Irreversibility in quantum maps with decoherence