Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy
As recently manifested [ 1 ], the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aba652 |
| _version_ | 1797750356637122560 |
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| author | Samy Mailoud Fausto Borgonovi Felix M Izrailev |
| author_facet | Samy Mailoud Fausto Borgonovi Felix M Izrailev |
| author_sort | Samy Mailoud |
| collection | DOAJ |
| description | As recently manifested [ 1 ], the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in a chaotic structure of the many-body eigenstates considered in the non-interacting basis. The semi-analytical approach used here, allows one to estimate the rate of the exponential growth as well as the relaxation time, after which the equilibration (thermalization) emerges. The key ingredient parameter in the description of this process is the width Γ of the local density of states (LDoS) defined by the initially excited state, the number of particles and the interaction strength. In this paper we show that apart from the meaning of Γ as the decay rate of survival probability, the width of the LDoS is directly related to the diagonal entropy and the latter can be linked to the thermodynamic entropy of a system equilibrium state emerging after the complete relaxation. The analytical expression relating the two entropies is derived phenomenologically and numerically confirmed in a model of bosons with random two-body interaction, as well as in a deterministic model which becomes completely integrable in the continuous limit. |
| first_indexed | 2024-03-12T16:32:33Z |
| format | Article |
| id | doaj.art-844abb8ecf4d4ac7a9a145c690137d2c |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:32:33Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
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| series | New Journal of Physics |
| spelling | doaj.art-844abb8ecf4d4ac7a9a145c690137d2c2023-08-08T15:26:24ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122808308710.1088/1367-2630/aba652Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropySamy Mailoud0https://orcid.org/0000-0001-6173-5762Fausto Borgonovi1https://orcid.org/0000-0002-9730-1189Felix M Izrailev2https://orcid.org/0000-0003-0326-2017Instituto de Física, Benemérita Universidad Autónoma de Puebla , Apartado Postal J-48, Puebla 72570, MexicoDipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica , via Musei 41, 25121 Brescia, Italy; Istituto Nazionale di Fisica Nucleare , Sezione di Pavia, via Bassi 6, I-27100, Pavia, ItalyInstituto de Física, Benemérita Universidad Autónoma de Puebla , Apartado Postal J-48, Puebla 72570, Mexico; NSCL and Department of Physics and Astronomy, Michigan State University , E Lansing, Michigan 48824-1321, United States of AmericaAs recently manifested [ 1 ], the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in a chaotic structure of the many-body eigenstates considered in the non-interacting basis. The semi-analytical approach used here, allows one to estimate the rate of the exponential growth as well as the relaxation time, after which the equilibration (thermalization) emerges. The key ingredient parameter in the description of this process is the width Γ of the local density of states (LDoS) defined by the initially excited state, the number of particles and the interaction strength. In this paper we show that apart from the meaning of Γ as the decay rate of survival probability, the width of the LDoS is directly related to the diagonal entropy and the latter can be linked to the thermodynamic entropy of a system equilibrium state emerging after the complete relaxation. The analytical expression relating the two entropies is derived phenomenologically and numerically confirmed in a model of bosons with random two-body interaction, as well as in a deterministic model which becomes completely integrable in the continuous limit.https://doi.org/10.1088/1367-2630/aba652thermalizationisolated quantum many-body systemsquantum chaos |
| spellingShingle | Samy Mailoud Fausto Borgonovi Felix M Izrailev Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy New Journal of Physics thermalization isolated quantum many-body systems quantum chaos |
| title | Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy |
| title_full | Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy |
| title_fullStr | Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy |
| title_full_unstemmed | Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy |
| title_short | Process of equilibration in many-body isolated systems: diagonal versus thermodynamic entropy |
| title_sort | process of equilibration in many body isolated systems diagonal versus thermodynamic entropy |
| topic | thermalization isolated quantum many-body systems quantum chaos |
| url | https://doi.org/10.1088/1367-2630/aba652 |
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