Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

We reexamine the problem of the ``Loschmidt echo, '' that measures the sensitivity to perturbation of quantum-chaotic dynamics. The overlap squared M (t) of two wave packets evolving under slightly different Hamiltonian is shown to have the double-exponential initial decay (-constante^2{₀t}) in the main part of the phase space. The coefficient ₀ is the self-averaging Lyapunov exponent. The average decay Me^-{₁t} is single exponential with a different coefficient ₁. The volume of phase space that contributes to M vanishes in the classical limit 0 for times less than the Ehrenfest time ₄=12₀^-1|ln|. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.