Mesoscopic Fluctuations of the Loschmidt Echo

Details Mesoscopic Fluctuations of the Loschmidt Echo Mesoscopic Fluctuations of the Loschmidt Echo

2004-10-13

arxiv.org/abs/quant-ph/0410099v2

Phys. Rev. E 71, 036223 (2005)

Physics

Quantum Physics

Final, extended version; to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.71.036223

We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket 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 $\hbar_{\rm eff}$, this decay is given by the sum of a classical term $\simeq \exp[-2 \lambda t]$, a quantum term $\simeq 2 \hbar_{\rm eff} \exp[-\Gamma t]$ and a mixed term $\simeq 2 \exp[-(\Gamma+\lambda)t]$. 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.

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