Fidelity Decay in Chaotical and Random Systems

Abstract

Fidelity is the overlap of wave functions with the same initial state propagated in time by slightly di erent Hamiltonians. Its behavior depends crucially on the choice of the initial wave function state. We review two cases: rst, the initial state is random. In this case a simple analytic relation with parametric spectral correlations can be established. The latter quantity is completely determined by the spectral data and can therefore be measured, without knowledge about the wave function. Second, the initial state is an eigenstate of the unperturbed system. In this case delity is identical to the survival probability. We nd unexpected features like revival and non-ergodicity. In this case uctuations around the mean are large and the full delity distribution becomes a non-trivial function. The full delity distribution can be calculated in the long time limit and for small perturbations.