Quantum freeze of fidelity decay for a class of integrable dynamics

Abstract

We discuss quantum fidelity decay of classically regular dynamics, in particular for animportant special case of a vanishing time-averaged perturbation operator, i.e. vanishingexpectation values of the perturbation in the eigenbasis of unperturbed dynamics. Acomplete semiclassical picture of this situation is derived in which we show that thequantum fidelity of individual coherent initial states exhibits three different regimes intime: (i) first it follows the corresponding classical fidelity up to time , (ii) then it freezes on a plateau of constant value, (iii) and after a timescale it exhibits fast ballistic decay as where is a strength of perturbation. All the constants are computed in terms of classicaldynamics for sufficiently small effective value of the Planck constant. A similar picture is worked out also for general initial states, andspecifically for random initial states, where , and . This prolonged stability 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 kickedtop.