TY - JOUR

T1 - Full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti model

AU - Bettelheim, Eldad

AU - Smith, Naftali R.

AU - Meerson, Baruch

N1 - Publisher Copyright:
© 2022 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - We investigate non-stationary heat transfer in the Kipnis-Marchioro-Presutti (KMP) lattice gas model at long times in one dimension when starting from a localized heat distribution. At large scales this initial condition can be described as a delta-function, u(x, t = 0) = Wδ(x). We characterize the process by the heat transferred to the right of a specified point x = X by time T, J = ∫ X ∞ u ( x , t = T ) d x , and study the full probability distribution P ( J , X , T ) . The particular case of X = 0 has been recently solved by Bettelheim et al (2022 Phys. Rev. Lett. 128 130602). At fixed J, the distribution P as a function of X and T has the same long-time dynamical scaling properties as the position of a tracer in a single-file diffusion. Here we evaluate P ( J , X , T ) by exploiting the recently uncovered complete integrability of the equations of the macroscopic fluctuation theory (MFT) for the KMP model and using the Zakharov-Shabat inverse scattering method. We also discuss asymptotics of P ( J , X , T ) which we extract from the exact solution and also obtain by applying two different perturbation methods directly to the MFT equations.

AB - We investigate non-stationary heat transfer in the Kipnis-Marchioro-Presutti (KMP) lattice gas model at long times in one dimension when starting from a localized heat distribution. At large scales this initial condition can be described as a delta-function, u(x, t = 0) = Wδ(x). We characterize the process by the heat transferred to the right of a specified point x = X by time T, J = ∫ X ∞ u ( x , t = T ) d x , and study the full probability distribution P ( J , X , T ) . The particular case of X = 0 has been recently solved by Bettelheim et al (2022 Phys. Rev. Lett. 128 130602). At fixed J, the distribution P as a function of X and T has the same long-time dynamical scaling properties as the position of a tracer in a single-file diffusion. Here we evaluate P ( J , X , T ) by exploiting the recently uncovered complete integrability of the equations of the macroscopic fluctuation theory (MFT) for the KMP model and using the Zakharov-Shabat inverse scattering method. We also discuss asymptotics of P ( J , X , T ) which we extract from the exact solution and also obtain by applying two different perturbation methods directly to the MFT equations.

KW - classical integrability

KW - fluctuating hydrodynamics

KW - macroscopic fluctuation theory

KW - transport processes/heat transfer

UR - http://www.scopus.com/inward/record.url?scp=85138978526&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/ac8a4d

DO - 10.1088/1742-5468/ac8a4d

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AN - SCOPUS:85138978526

SN - 1742-5468

VL - 2022

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 9

M1 - 093103

ER -