TY - JOUR

T1 - Complete integrability of the problem of full statistics of nonstationary mass transfer in the simple inclusion process

AU - Bettelheim, Eldad

AU - Meerson, Baruch

N1 - Publisher Copyright:
© 2024 American Physical Society.

PY - 2024/7

Y1 - 2024/7

N2 - The simple inclusion process (SIP) interpolates between two well-known lattice gas models: the independent random walkers and the Kipnis-Marchioro-Presutti model. Here we study large deviations of nonstationary mass transfer in the SIP at long times in one dimension. We suppose that N≫1 particles start from a single lattice site at the origin, and we are interested in the probability P(M,N,T) of observing M of the particles, 0≤M≤N, to the right of the origin at a specified time T≫1. At large times, the corresponding full probability distribution has a large-deviation behavior, -lnP(M,N,T)≃Ts(M/N,N/T). We determine the rate function s exactly by uncovering and utilizing complete integrability, by the inverse scattering method, of the underlying equations of the macroscopic fluctuation theory. We also analyze different asymptotic limits of the rate function s.

AB - The simple inclusion process (SIP) interpolates between two well-known lattice gas models: the independent random walkers and the Kipnis-Marchioro-Presutti model. Here we study large deviations of nonstationary mass transfer in the SIP at long times in one dimension. We suppose that N≫1 particles start from a single lattice site at the origin, and we are interested in the probability P(M,N,T) of observing M of the particles, 0≤M≤N, to the right of the origin at a specified time T≫1. At large times, the corresponding full probability distribution has a large-deviation behavior, -lnP(M,N,T)≃Ts(M/N,N/T). We determine the rate function s exactly by uncovering and utilizing complete integrability, by the inverse scattering method, of the underlying equations of the macroscopic fluctuation theory. We also analyze different asymptotic limits of the rate function s.

UR - http://www.scopus.com/inward/record.url?scp=85197649114&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.110.014101

DO - 10.1103/PhysRevE.110.014101

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AN - SCOPUS:85197649114

SN - 2470-0045

VL - 110

JO - Physical Review E

JF - Physical Review E

IS - 1

M1 - 014101

ER -