Mesoscopic fluctuations of the Loschmidt echo

[en] We investigate the time-dependent variance of the fidelity with which an initial narrow wave packet is reconstructed after its dynamics is time reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time t(c), after which it decays. To leading order in the effective Planck's constant h(eff), this decay is given by the sum of a classical term similar or equal to exp[-2 lambda t], a quantum term similar or equal to 2h(eff) exp[-Gamma t], and a mixed term similar or equal to 2 exp[-(Gamma+lambda)t]. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent lambda in a larger parameter range. Our results are confirmed by numerical simulations.

Disciplines :

Physics

Author, co-author :

Petitjean, Cyril ; Université de Liège - ULiège > Département de physique > Physique quantique statistique

Jacquod, P.

Language :

English

Title :

Mesoscopic fluctuations of the Loschmidt echo

Publication date :

2005

Journal title :

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

ISSN :

1539-3755

eISSN :

1550-2376

Publisher :

American Physical Soc, College Pk, United States - Maryland

Volume :

Issue :

Pages :

036223-6

Peer reviewed :

Peer Reviewed verified by ORBi

Commentary :

Available on ORBi :

since 04 December 2013

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