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Quantum freeze of fidelity decay for a class of integrable dynamics | | Tomaz Prosen
; Marko Znidaric
; | | Date: |
13 Jun 2003 | | Journal: | New Journal of Physics 5 (2003) 109 | | Subject: | Quantum Physics; Chaotic Dynamics; Exactly Solvable and Integrable Systems | quant-ph nlin.CD nlin.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 t1=hbar^(-1/2), (ii) then it freezes on a plateau of constant value, (iii) and after a time scale t_2=min[hbar^(1/2) delta^(-2),hbar^(-1/2) delta^(-1)] it exhibits fast ballistic decay as exp(-const. 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=1, and t_2=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 top. | | Source: | arXiv, quant-ph/0306097 | | Services: | Forum | Review | PDF | Favorites | |
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