Lyapunov decay in quantum irreversibility
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 perturba...
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paper:paper_1364503X_v374_n2069_p_GarciaMata2023-06-08T16:11:41Z Lyapunov decay in quantum irreversibility García-Mata, Ignacio Roncaglia, Augusto José Wisniacki, Diego A. Foundations of quantum mechanics Irreversibility Quantum chaos Chaotic systems Hilbert spaces Lyapunov methods Foundations of quantum mechanics Function of time Infinite dimensional Irreversibility Loschmidt echoes Lyapunov exponent Perturbation strength Quantum chaos Quantum theory 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. © 2016 The Author(s) Published by the Royal Society. All rights reserved. Fil:García-Mata, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Roncaglia, A.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wisniacki, D.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1364503X_v374_n2069_p_GarciaMata http://hdl.handle.net/20.500.12110/paper_1364503X_v374_n2069_p_GarciaMata |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Foundations of quantum mechanics Irreversibility Quantum chaos Chaotic systems Hilbert spaces Lyapunov methods Foundations of quantum mechanics Function of time Infinite dimensional Irreversibility Loschmidt echoes Lyapunov exponent Perturbation strength Quantum chaos Quantum theory |
| spellingShingle |
Foundations of quantum mechanics Irreversibility Quantum chaos Chaotic systems Hilbert spaces Lyapunov methods Foundations of quantum mechanics Function of time Infinite dimensional Irreversibility Loschmidt echoes Lyapunov exponent Perturbation strength Quantum chaos Quantum theory García-Mata, Ignacio Roncaglia, Augusto José Wisniacki, Diego A. Lyapunov decay in quantum irreversibility |
| topic_facet |
Foundations of quantum mechanics Irreversibility Quantum chaos Chaotic systems Hilbert spaces Lyapunov methods Foundations of quantum mechanics Function of time Infinite dimensional Irreversibility Loschmidt echoes Lyapunov exponent Perturbation strength Quantum chaos Quantum theory |
| description |
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. © 2016 The Author(s) Published by the Royal Society. All rights reserved. |
| author |
García-Mata, Ignacio Roncaglia, Augusto José Wisniacki, Diego A. |
| author_facet |
García-Mata, Ignacio Roncaglia, Augusto José Wisniacki, Diego A. |
| author_sort |
García-Mata, Ignacio |
| title |
Lyapunov decay in quantum irreversibility |
| title_short |
Lyapunov decay in quantum irreversibility |
| title_full |
Lyapunov decay in quantum irreversibility |
| title_fullStr |
Lyapunov decay in quantum irreversibility |
| title_full_unstemmed |
Lyapunov decay in quantum irreversibility |
| title_sort |
lyapunov decay in quantum irreversibility |
| publishDate |
2016 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1364503X_v374_n2069_p_GarciaMata http://hdl.handle.net/20.500.12110/paper_1364503X_v374_n2069_p_GarciaMata |
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AT garciamataignacio lyapunovdecayinquantumirreversibility AT roncagliaaugustojose lyapunovdecayinquantumirreversibility AT wisniackidiegoa lyapunovdecayinquantumirreversibility |
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