Lax random matrices from Calogero systems
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916755033554944 |
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| author | Kethepalli, Jitendra Kulkarni, Manas Kundu, Anupam Spohn, Herbert |
| author_facet | Kethepalli, Jitendra Kulkarni, Manas Kundu, Anupam Spohn, Herbert |
| contents | We study a class of random matrices arising from the Lax matrix structure of classical integrable systems, particularly the Calogero family of models. Our focus is the density of eigenvalues for these random matrices. The problem can be mapped to analyzing the density of eigenvalues for generalized versions of conventional random matrix ensembles, including a modified form of the log-gas. The mapping comes from the underlying integrable structure of these models. Such deep connection is confirmed by extensive Monte-Carlo simulations. Thereby we move forward not only in terms of understanding such class of random matrices arising from integrable many-body systems, but also by providing a building block for the generalized hydrodynamic description of integrable systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13254 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lax random matrices from Calogero systems Kethepalli, Jitendra Kulkarni, Manas Kundu, Anupam Spohn, Herbert Statistical Mechanics We study a class of random matrices arising from the Lax matrix structure of classical integrable systems, particularly the Calogero family of models. Our focus is the density of eigenvalues for these random matrices. The problem can be mapped to analyzing the density of eigenvalues for generalized versions of conventional random matrix ensembles, including a modified form of the log-gas. The mapping comes from the underlying integrable structure of these models. Such deep connection is confirmed by extensive Monte-Carlo simulations. Thereby we move forward not only in terms of understanding such class of random matrices arising from integrable many-body systems, but also by providing a building block for the generalized hydrodynamic description of integrable systems. |
| title | Lax random matrices from Calogero systems |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2411.13254 |