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2016 ; 374
(2069
): ä Nephropedia Template TP
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Lyapunov decay in quantum irreversibility
#MMPMID27140966
García-Mata I
; Roncaglia AJ
; Wisniacki DA
Philos Trans A Math Phys Eng Sci
2016[Jun]; 374
(2069
): ä PMID27140966
show ga
The Loschmidt echo--also known as fidelity--is a very useful tool to study
irreversibility in quantum mechanics due to perturbations or imperfections. Many
different regimes, as a function of time and strength of the perturbation, have
been identified. For chaotic systems, there is a range of perturbation strengths
where the decay of the Loschmidt echo is perturbation independent, and given by
the classical Lyapunov exponent. But observation of the Lyapunov decay depends
strongly on the type of initial state upon which an average is carried out. This
dependence can be removed by averaging the fidelity over the Haar measure, and
the Lyapunov regime is recovered, as has been shown for quantum maps. In this
work, we introduce an analogous quantity for systems with infinite dimensional
Hilbert space, in particular the quantum stadium billiard, and we show clearly
the universality of the Lyapunov regime.