Current fluctuations in a partially asymmetric simple exclusion process with a defect particle

Abstract

We study an exclusion process on a ring comprising a free defect particle in a bath of normal particles. The model is one of the few integrable cases in which the bath particles are partially asymmetric. The presence of the free defect creates localized or shock phases according to parameter values. We use a functional approach to Bethe equations resulting from a nested Bethe ansatz to calculate exactly the mean currents and diffusion constants. The results agree very well with Monte Carlo simulations and reveal the main modes of fluctuation in the different phases of the steady state. Published by the American Physical Society 2024

KPZ fluctuations in finite volume

“…An inclusion property for the spectrum when varying the number of species [582] has allowed to confirm a numerical prediction [583] that the spectral gap behaves according to KPZ scaling, with dynamical exponent z = 3/2. The average value of the current of each type of particle in the stationary state is also known [506] from Bethe Ansatz, but higher cumulants of the currents are still missing, except for the case of a single particle of second type [552,584].…”