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For a prepared state exact expressions for the time dependent mean fidelityas well as for the mean inverse paricipation ratio are obtained analytically.The distribution function of fidelity in the long time limit and of inverseparticipation ratio are studied numerically and analytically. Surprisingfeatures like fidelity revival and enhanced non--ergodicity are observed. Therole of the coupling coefficients and of complexity of background is studied aswell.

Exact Fidelity and Full Fidelity Statistics in Regular and Chaotic Surroundings