Recovery of the fidelity amplitude for the Gaussian ensembles

Abstract

Using supersymmetry techniques analytical expressions for 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) > are obtained, where H_epsilon=H_0+(sqrt{epsilon}/(2 pi) )*V, and H_0 and H_epsilon are taken from the Gaussian unitary ensemble (GUE) or the Gaussian orthogonal ensemble (GOE), respectively. As long as the perturbation strength is small compared to the mean level spacing, a Gaussian decay of the fidelity amplitude is observed, whereas for stronger perturbations a change to a single-exponential decay takes place, in accordance with results from literature. Close to the Heisenberg time tau=1, however, a partial revival of the fidelity is found, which hitherto remained unnoticed. Random matrix simulations have been performed for the three Gaussian ensembles. For the case of the GOE and the GUE they are in perfect agreement with the analytical results.

revised version, 18 pages, 7 figures

References in corpus (5)

• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• A random matrix formulation of fidelity decay
• Theory of quantum Loschmidt echoes
• Signatures of the correlation hole in total and partial cross sections

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