Origin of the exponential decay of the Loschmidt echo in integrable systems

Remy Dubertrand, Arseni Goussev

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
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Abstract

We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state. In particular, we show that the decay rate, unlike in the case of the chaotic dynamics, is directly proportional to the strength of the Hamiltonian perturbation. Finally, we compare our analytical predictions against the results of a numerical computation of the Loschmidt echo for a quantum particle moving inside a one-dimensional box with Dirichlet-Robin boundary conditions, and find the two in good agreement.
Original languageEnglish
Pages (from-to)022915
JournalPhysical Review E
Volume89
Issue number2
DOIs
Publication statusPublished - 18 Feb 2014

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