dorsal/arxiv
View SchemaQuantum freeze of fidelity decay for a class of integrable dynamics
| Authors | Tomaz Prosen, Marko Znidaric |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306097 |
| URL | https://arxiv.org/abs/quant-ph/0306097 |
| DOI | 10.1088/1367-2630/5/1/109 |
| Journal | New Journal of Physics 5 (2003) 109 |
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.
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"abstract": "We discuss quantum fidelity decay of classically regular dynamics, in\nparticular for an important special case of a vanishing time averaged\nperturbation operator, i.e. vanishing expectation values of the perturbation in\nthe eigenbasis of unperturbed dynamics. A complete semiclassical picture of\nthis situation is derived in which we show that the quantum fidelity of\nindividual coherent initial states exhibits three different regimes in time:\n(i) first it follows the corresponding classical fidelity up to time\nt1=hbar^(-1/2), (ii) then it freezes on a plateau of constant value, (iii) and\nafter a time scale t_2=min[hbar^(1/2) delta^(-2),hbar^(-1/2) delta^(-1)] it\nexhibits fast ballistic decay as exp(-const. delta^4 t^2/hbar) where delta is a\nstrength of perturbation. All the constants are computed in terms of classical\ndynamics for sufficiently small effective value hbar of the Planck constant. A\nsimilar picture is worked out also for general initial states, and specifically\nfor random initial states, where t_1=1, and t_2=delta^(-1). This prolonged\nstability of quantum dynamics in the case of a vanishing time averaged\nperturbation could prove to be useful in designing quantum devices. Theoretical\nresults are verified by numerical experiments on the quantized integrable top.",
"arxiv_id": "quant-ph/0306097",
"authors": [
"Tomaz Prosen",
"Marko Znidaric"
],
"categories": [
"quant-ph",
"nlin.CD",
"nlin.SI"
],
"doi": "10.1088/1367-2630/5/1/109",
"journal_ref": "New Journal of Physics 5 (2003) 109",
"title": "Quantum freeze of fidelity decay for a class of integrable dynamics",
"url": "https://arxiv.org/abs/quant-ph/0306097"
},
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