Fidelity recovery in chaotic systems and the Debye-Waller factor

Details Fidelity recovery in chaotic systems and the Debye-Waller factor Fidelity recovery in chaotic systems and the Debye-Waller factor

2004-09-09

arxiv.org/abs/nlin/0409021v2

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevLett.94.244101

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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