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Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems
The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the sys...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9321331/ https://www.ncbi.nlm.nih.gov/pubmed/35885182 http://dx.doi.org/10.3390/e24070959 |
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author | Weidenmüller, Hans A. |
author_facet | Weidenmüller, Hans A. |
author_sort | Weidenmüller, Hans A. |
collection | PubMed |
description | The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given. |
format | Online Article Text |
id | pubmed-9321331 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-93213312022-07-27 Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems Weidenmüller, Hans A. Entropy (Basel) Article The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given. MDPI 2022-07-11 /pmc/articles/PMC9321331/ /pubmed/35885182 http://dx.doi.org/10.3390/e24070959 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Weidenmüller, Hans A. Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems |
title | Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems |
title_full | Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems |
title_fullStr | Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems |
title_full_unstemmed | Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems |
title_short | Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems |
title_sort | quantum chaos, random matrices, and irreversibility in interacting many-body quantum systems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9321331/ https://www.ncbi.nlm.nih.gov/pubmed/35885182 http://dx.doi.org/10.3390/e24070959 |
work_keys_str_mv | AT weidenmullerhansa quantumchaosrandommatricesandirreversibilityininteractingmanybodyquantumsystems |