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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2310.13392 |
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| _version_ | 1866909307690287104 |
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| author | Prazeres, Luis Fernando dos de Oliveira, Thiago R. |
| author_facet | Prazeres, Luis Fernando dos de Oliveira, Thiago R. |
| contents | It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found and the phenomenon was named weak thermalization. Later, it was argued that such oscillations will eventually decay suggesting that weak thermalization was about time scales and not the size of the fluctuations. Nevertheless, the analyses of the size of the fluctuations were more qualitative. Here, using exact diagonalization we analyze how the size of the typical fluctuation, after long enough time for equilibration to happen, scales with the system size. For that, we use rigorous mathematical upper bounds on the equilibration of isolated quantum systems. We show that weak thermalization can be understood to be due to the small effective dimension of the initial state. Furthermore, we show that the fluctuations decay exponentially with the system size for both weak and strong thermalization indicating no sharp transitions between these two regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13392 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smooth Crossover Between Weak and Strong Thermalization using Rigorous Bounds on Equilibration of Isolated Systems Prazeres, Luis Fernando dos de Oliveira, Thiago R. Quantum Physics It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found and the phenomenon was named weak thermalization. Later, it was argued that such oscillations will eventually decay suggesting that weak thermalization was about time scales and not the size of the fluctuations. Nevertheless, the analyses of the size of the fluctuations were more qualitative. Here, using exact diagonalization we analyze how the size of the typical fluctuation, after long enough time for equilibration to happen, scales with the system size. For that, we use rigorous mathematical upper bounds on the equilibration of isolated quantum systems. We show that weak thermalization can be understood to be due to the small effective dimension of the initial state. Furthermore, we show that the fluctuations decay exponentially with the system size for both weak and strong thermalization indicating no sharp transitions between these two regimes. |
| title | Smooth Crossover Between Weak and Strong Thermalization using Rigorous Bounds on Equilibration of Isolated Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.13392 |