Quantum freeze of fidelity decay for a class of integrable dynamics

We discuss quantum fidelity decay of classically regular dynamics, in particular for an important special case of a vanishing time-averaged perturbation operator, i.e. vanishing expectation values of the perturbation in the eigenbasis of unperturbed dynamics. A complete semiclassical picture of this situation is derived in which we show that the quantum fidelity of individual coherent initial states exhibits three different regimes in time: (i) first it follows the corresponding classical fidelity up to time t(1) similar to (h) over bar (-1/2), (ii) then it freezes on a plateau of constant value, (iii) and after a timescale t(2) similar to min{(h) over bar (1/2) delta(-2), (h) over bar (-1/2) delta(-1)} it exhibits fast ballistic decay as exp(- constant x delta(4)t(2)/(h) over bar) where delta is a strength of perturbation. All the constants are computed in terms of classical dynamics for sufficiently small effective value (h) over bar of the Planck constant. A similar picture is worked out also for general initial states, and specifically for random initial states, where t(1) similar to 1, and t(2) similar to delta(-1). This prolonged stability of quantum dynamics in the case of a vanishing time-averaged perturbation could prove to be useful in designing quantum devices. Theoretical results are verified by numerical experiments on the quantized integrable kicked top.