Integrable fishnet circuits and Brownian solitons
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918101981855744 |
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| author | Krajnik, Žiga Ilievski, Enej Prosen, Tomaž Héry, Benjamin J. A. Pasquier, Vincent |
| author_facet | Krajnik, Žiga Ilievski, Enej Prosen, Tomaž Héry, Benjamin J. A. Pasquier, Vincent |
| contents | We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a `fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable fishnet circuits and Brownian solitons Krajnik, Žiga Ilievski, Enej Prosen, Tomaž Héry, Benjamin J. A. Pasquier, Vincent Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a `fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion. |
| title | Integrable fishnet circuits and Brownian solitons |
| topic | Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.08030 |