Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866911202971484160 |
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| author | Bettelheim, Eldad Smith, Naftali R. Meerson, Baruch |
| author_facet | Bettelheim, Eldad Smith, Naftali R. Meerson, Baruch |
| contents | We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by Kaup and Newell (1978) for the DNLS. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_02474 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model Bettelheim, Eldad Smith, Naftali R. Meerson, Baruch Statistical Mechanics Probability Exactly Solvable and Integrable Systems We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by Kaup and Newell (1978) for the DNLS. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation. |
| title | Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model |
| topic | Statistical Mechanics Probability Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2112.02474 |