Fidelity Recovery in Chaotic Systems and the Debye-Waller Factor

H.-J. Stöckmann and R. Schäfer
Phys. Rev. Lett. 94, 244101 – Published 20 June 2005

Abstract

Using supersymmetry calculations and random matrix simulations, we study the decay of the average of the fidelity amplitude fϵ(τ)=ψ(0)|exp(2πiHϵτ)exp(2πiH0τ)|ψ(0), where Hϵ differs from H0 by a slight perturbation characterized by the parameter ϵ. For strong perturbations a recovery of fϵ(τ) at the Heisenberg time τ=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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  • Received 27 July 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.244101

©2005 American Physical Society

Authors & Affiliations

H.-J. Stöckmann and R. Schäfer

  • Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany

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Issue

Vol. 94, Iss. 24 — 24 June 2005

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