Quantum Corrections to Fidelity Decay in Chaotic Systems

Abstract

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying perturbations. Moreover, using trajectory-based methods we show a relation, recently obtained in RMT, between the fidelity amplitude and the cross-form factor for parametric level correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity amplitude. Furthermore our semiclassical approach allows for a unified treatment of the fidelity, both in the Fermi golden rule and Lyapunov regimes, demonstrating that quantum corrections are suppressed in the latter.

14 pages, 4 figures

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Cited by in corpus (13)

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• Efficient semiclassical approach for time delays
• Conductance fluctuations in chaotic systems with tunnel barriers
• Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
• Lyapunov Decoherence Rate in Classically Chaotic Systems
• Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials
• Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents
• Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown
• Scattering approach to fidelity decay in closed systems and parametric level correlations
• Partial thermalisation of a two-state system coupled to a finite quantum bath
• Parametric Number Covariance in Quantum Chaotic Spectra