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We address the sensitivity of quantum mechanical time evolution byconsidering the time decay of the Loschmidt echo (LE) (or fidelity) for localperturbations of the Hamiltonian. Within a semiclassical approach we deriveanalytical expressions for the LE decay for chaotic systems for the whole rangefrom weak to strong local perturbations and identify different decay regimeswhich complement those known for the case of global perturbations. For weakperturbations a Fermi-golden-rule (FGR) type behavior is recovered. For strongperturbations the escape-rate regime is reached, where the LE decaysexponentially with a rate independent of the perturbation strength. Thetransition between the FGR regime and the escape-rate regime is non-monotonic,i.e. the rate of the exponential time-decay of the LE oscillates as a functionof the perturbation strength. We further perform extensive quantum mechanicalcalculations of the LE based on numerical wave packet evolution which stronglysupport our semiclassical theory. Finally, we discuss in some detail possibleexperimental realizations for observing the predicted behavior of the LE.

Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime