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Pré-Publication, Document De Travail Année : 2017

The quantum Loschmidt echo on flat tori

Résumé

The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit formulae for this quantity in the transition regime where it is expected to decay in the semiclassical limit. The expression involves both a two-microlocal defect measure of the initial data and the form of the perturbation. As an application, we exhibit a non-concentration criterium on the sequence of initial data under which one does not observe a macroscopic decay of the Quantum Loschmidt Echo. We also apply our results to several examples of physically relevant initial data such as coherent states and plane waves.
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Dates et versions

hal-01643206 , version 1 (23-11-2017)

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Gabriel Rivière, Henrik Ueberschaer. The quantum Loschmidt echo on flat tori. 2017. ⟨hal-01643206⟩
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