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We discuss quantum fidelity decay of classically regular dynamics, inparticular for an important special case of a vanishing time averagedperturbation operator, i.e. vanishing expectation values of the perturbation inthe eigenbasis of unperturbed dynamics. A complete semiclassical picture ofthis situation is derived in which we show that the quantum fidelity ofindividual coherent initial states exhibits three different regimes in time:(i) first it follows the corresponding classical fidelity up to timet1=hbar^(-1/2), (ii) then it freezes on a plateau of constant value, (iii) andafter a time scale t_2=min[hbar^(1/2) delta^(-2),hbar^(-1/2) delta^(-1)] itexhibits fast ballistic decay as exp(-const. delta^4 t^2/hbar) where delta is astrength of perturbation. All the constants are computed in terms of classicaldynamics for sufficiently small effective value hbar of the Planck constant. Asimilar picture is worked out also for general initial states, and specificallyfor random initial states, where t_1=1, and t_2=delta^(-1). This prolongedstability of quantum dynamics in the case of a vanishing time averagedperturbation could prove to be useful in designing quantum devices. Theoreticalresults are verified by numerical experiments on the quantized integrable top.

Quantum freeze of fidelity decay for a class of integrable dynamics