Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917659388411904 |
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| author | Ammari, Zied Farhat, Shahnaz Petrat, Sören |
| author_facet | Ammari, Zied Farhat, Shahnaz Petrat, Sören |
| contents | We consider the many-body quantum Gibbs state for the Bose-Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of the average particle number. For this model it is known that the many-body Gibbs state converges, as temperature goes to infinity, to the Gibbs measure of a discrete nonlinear Schrödinger equation, i.e., a Gibbs measure defined in terms of a one-body theory. In this article we extend these results by proving an expansion to any order of the many-body Gibbs state with inverse temperature as a small parameter. The coefficients in the expansion can be calculated as vacuum expectation values using a recursive formula, and we compute the first two coefficients explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph Ammari, Zied Farhat, Shahnaz Petrat, Sören Mathematical Physics We consider the many-body quantum Gibbs state for the Bose-Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of the average particle number. For this model it is known that the many-body Gibbs state converges, as temperature goes to infinity, to the Gibbs measure of a discrete nonlinear Schrödinger equation, i.e., a Gibbs measure defined in terms of a one-body theory. In this article we extend these results by proving an expansion to any order of the many-body Gibbs state with inverse temperature as a small parameter. The coefficients in the expansion can be calculated as vacuum expectation values using a recursive formula, and we compute the first two coefficients explicitly. |
| title | Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2405.04055 |