Quantum freeze of fidelity decay

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

Quantum freeze of fidelity decay for a class of integrable dynamics

Tomaž Prosen et al 2003 New J. Phys. 5 109 doi: 10.1088/1367-2630/5/1/109

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Tomaž Prosen and Marko Žnidarič
Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
E-mail: prosen@fiz.uni-lj.si and znidaricm@fiz.uni-lj.si

Abstract. 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.

Received 27 June 2003
Published 21 August 2003

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Quantum freeze of fidelity decay for a class of integrable dynamics

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