Quantum freeze of fidelity decay for a class of integrable dynamics

doi:10.1088/1367-2630/5/1/109

New Journal of Physics

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New Journal of Physics Volume 5 2003 Create an alert RSS this journal

Tomaž Prosen and Marko Žnidarič 2003 New J. Phys. 5 109 doi:10.1088/1367-2630/5/1/109

Quantum freeze of fidelity decay for a class of integrable dynamics

Tomaž Prosen and Marko Žnidarič

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Abstract References Cited By Supplementary Data

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 $t_1 \sim \hbar ^{-1/2}$ , (ii) then it freezes on a plateau of constant value, (iii) and after a timescale $t_2 \sim \min \{\hbar^{1/2}\delta^{-2},\hbar^{-1/2}\delta^{-1}\}$ it exhibits fast ballistic decay as $\exp (-{\mathrm {constant}}\times \delta^4 t^2/\hbar)$ where $\delta$ is a strength of perturbation. All the constants are computed in terms of classical dynamics for sufficiently small effective value $\hbar$ of the Planck constant. A similar picture is worked out also for general initial states, and specifically for random initial states, where $t_1 \sim 1$ , and $t_2 \sim \delta^{-1}$ . 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.