Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
| Autor: | Eldad Bettelheim, Naftali R. Smith, Baruch Meerson |
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| Rok vydání: | 2022 |
| Předmět: |
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Statistical Mechanics (cond-mat.stat-mech) Probability (math.PR) FOS: Mathematics FOS: Physical sciences General Physics and Astronomy Nonlinear Sciences::Pattern Formation and Solitons Condensed Matter - Statistical Mechanics Mathematics - Probability |
| Zdroj: | Physical Review Letters. 128 |
| ISSN: | 1079-7114 0031-9007 |
| Popis: | 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 Schr\"{o}dinger 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. Comment: 9 pages, including Supplemental Material, 5 figures |
| Databáze: | OpenAIRE |
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