Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application
We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ‘state-dependent’ rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quan...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ace470 |
| _version_ | 1797748631109894144 |
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| author | Eliana Fiorelli Markus Müller Igor Lesanovsky Federico Carollo |
| author_facet | Eliana Fiorelli Markus Müller Igor Lesanovsky Federico Carollo |
| author_sort | Eliana Fiorelli |
| collection | DOAJ |
| description | We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ‘state-dependent’ rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-) local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models. |
| first_indexed | 2024-03-12T16:08:29Z |
| format | Article |
| id | doaj.art-6d403995b3bc430bb75d872fed9c45b6 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:08:29Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-6d403995b3bc430bb75d872fed9c45b62023-08-09T14:15:21ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125808301010.1088/1367-2630/ace470Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and applicationEliana Fiorelli0https://orcid.org/0000-0003-4677-3204Markus Müller1https://orcid.org/0000-0002-2813-3097Igor Lesanovsky2https://orcid.org/0000-0001-9660-9467Federico Carollo3https://orcid.org/0000-0002-6961-7143Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), UIB-CSIC, UIB Campus , Palma de Mallorca 07122, Spain; Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich , 52428 Jülich, Germany; Institute for Quantum Information, RWTH Aachen University , 52056 Aachen, GermanyInstitute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich , 52428 Jülich, Germany; Institute for Quantum Information, RWTH Aachen University , 52056 Aachen, GermanyInstitut für Theoretische Physik, Universität Tübingen , Auf der Morgenstelle 14, 72076 Tübingen, Germany; School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham , Nottingham NG7 2RD, United KingdomInstitut für Theoretische Physik, Universität Tübingen , Auf der Morgenstelle 14, 72076 Tübingen, GermanyWe consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ‘state-dependent’ rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-) local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models.https://doi.org/10.1088/1367-2630/ace470quantum Hopfield neural networksmean-field dynamicsmany-body open quantum systems |
| spellingShingle | Eliana Fiorelli Markus Müller Igor Lesanovsky Federico Carollo Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application New Journal of Physics quantum Hopfield neural networks mean-field dynamics many-body open quantum systems |
| title | Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application |
| title_full | Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application |
| title_fullStr | Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application |
| title_full_unstemmed | Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application |
| title_short | Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application |
| title_sort | mean field dynamics of open quantum systems with collective operator valued rates validity and application |
| topic | quantum Hopfield neural networks mean-field dynamics many-body open quantum systems |
| url | https://doi.org/10.1088/1367-2630/ace470 |
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