Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model

Eldad Bettelheim, Naftali R. Smith, Baruch Meerson

Research output: Contribution to journalArticlepeer-review

Abstract

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 D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978)JMAPAQ0022-248810.1063/1.523737 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.

Original languageEnglish
Article number130602
JournalPhysical Review Letters
Volume128
Issue number13
DOIs
StatePublished - 1 Apr 2022

ASJC Scopus subject areas

  • Physics and Astronomy (all)

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