Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908375040655360 |
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| author | Meng, Zhi-Xuan Xu, Shuai-Xia Zhao, Yu-Qiu |
| author_facet | Meng, Zhi-Xuan Xu, Shuai-Xia Zhao, Yu-Qiu |
| contents | In the present paper, we study the time-dependent correlation function of the one-dimensional impenetrable Bose gas, which can be expressed in terms of the Fredholm determinant of a time-dependent sine kernel and the solutions of the separated NLS equations. We derive the large time and distance asymptotic expansions of this determinant and the solutions of the separated NLS equations in both the space-like region and time-like region of the $(x,t)$-plane. Furthermore, we observe a phase transition between the asymptotic expansions in these two different regions. The phase transition is then shown to be described by a particular solution of the Painlevé IV equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition Meng, Zhi-Xuan Xu, Shuai-Xia Zhao, Yu-Qiu Mathematical Physics Statistics Theory 35Q55 (33E17 34M55 35C20 82C10) In the present paper, we study the time-dependent correlation function of the one-dimensional impenetrable Bose gas, which can be expressed in terms of the Fredholm determinant of a time-dependent sine kernel and the solutions of the separated NLS equations. We derive the large time and distance asymptotic expansions of this determinant and the solutions of the separated NLS equations in both the space-like region and time-like region of the $(x,t)$-plane. Furthermore, we observe a phase transition between the asymptotic expansions in these two different regions. The phase transition is then shown to be described by a particular solution of the Painlevé IV equation. |
| title | Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition |
| topic | Mathematical Physics Statistics Theory 35Q55 (33E17 34M55 35C20 82C10) |
| url | https://arxiv.org/abs/2505.16780 |