Fidelity Decay in Chaotical and Random Systems
H. Kohler
Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juana de la Cruz 3, Cantoblanco, 28049 Madrid, Spain
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Fidelity is the overlap of wave functions with the same initial state propagated in time by slightly different Hamiltonians. Its behavior depends crucially on the choice of the initial wave function state. We review two cases: first, 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 fidelity is identical to the survival probability. We find unexpected features like revival and non-ergodicity. In this case fluctuations around the mean are large and the full fidelity distribution becomes a non-trivial function. The full fidelity distribution can be calculated in the long time limit and for small perturbations.
DOI: 10.12693/APhysPolA.120.A-119
PACS numbers: 05.30.-d, 03.65.Yz, 05.45.Mt, 73.23.-b