Fidelity recovery in chaotic systems and the Debye-Waller factor -: art. no. 244101

Using supersymmetry calculations and random matrix simulations, we study the decay of the average of the fidelity amplitude f(epsilon)(tau)=<psi(0)\exp(2 pi iH(epsilon)tau)exp(-2 pi iH(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.