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Fidelity recovery in chaotic systems and the Debye-Waller factor

H. -J. Stoeckmann·R. Schaefer
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Abstract

Using supersymmetry calculations and random matrix simulations, we studied the decay of the average of the fidelity amplitude f_epsilon(tau)= , 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.

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H. -J. Stoeckmann, R. Schaefer. 2005-05-13. Fidelity recovery in chaotic systems and the Debye-Waller factor. https://doi.org/10.1103/physrevlett.94.244101

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