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Mesoscopic fluctuations of the Loschmidt echo

Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland

Phys. Rev. E 71, 036223 – Published 29 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036223

Abstract

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 $ℏ_{eff}$ , this decay is given by the sum of a classical term $≃ \exp [- 2 λ t]$ , a quantum term $≃ 2 ℏ_{eff} \exp [- Γ t]$ , and a mixed term $≃ 2 \exp [- (Γ + λ) t]$ . Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $λ$ in a larger parameter range. Our results are confirmed by numerical simulations.

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References (29)

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Mesoscopic fluctuations of the Loschmidt echo

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