Fidelity recovery in chaotic systems and the Debye-Waller factor

Abstract

Using supersymmetry calculations and random matrix simulations, we studied the decay of the average of the fidelity amplitude f_epsilon(tau)=<psi(0)| exp(2 pi i H_epsilon tau) exp(-2 pi i H_0 tau) |psi(0)>, where H_epsilon differs from H_0 by a slight perturbation characterized by the parameter epsilon. For strong perturbations a recovery of f_epsilon(tau) at the Heisenberg time tau=1 is found. It is most pronounced for the Gaussian symplectic ensemble, and least for the Gaussian orthogonal one. Using Dyson's Brownian motion model for an eigenvalue crystal, the recovery is interpreted in terms of a spectral analogue of the Debye-Waller factor known from solid state physics, describing the decrease of X-ray and neutron diffraction peaks with temperature due to lattice vibrations.

revised version (major changes), 4 pages, 4 figures

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• Loschmidt Echo
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• Classical wave experiments on chaotic scattering
• Chaos and Complexity of quantum motion
• Fidelity amplitude of the scattering matrix in microwave cavities
• Decoherence of two qubit systems: A random matrix description
• Algebraic fidelity decay for local perturbations
• A random matrix theory of decoherence
• Quantum Corrections to Fidelity Decay in Chaotic Systems
• Surprising relations between parametric level correlations and fidelity decay
• Anomalous slow fidelity decay for symmetry breaking perturbations
• Single qubit decoherence under a separable coupling to a random matrix environment
• Engineering fidelity echoes in Bose-Hubbard Hamiltonians
• Improving coherence with nested environments
• First verification of generic fidelity recovery in a dynamical system
• Beyond Fermi's golden rule with the statistical Jacobi approximation
• A trivial observation on time reversal in random matrix theory
• Parametric correlations versus fidelity decay: the symmetry breaking case
• Survival Probability of a Doorway State in regular and chaotic environments
• 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
• One, Two, and $n$ Qubit Decoherence
• Parametric Number Covariance in Quantum Chaotic Spectra