DMRG-study of current and activity fluctuations near non-equilibrium phase transitions

TL;DR

This paper uses the DMRG method to analyze current fluctuations and activity near non-equilibrium phase transitions in stochastic systems, revealing scaling behaviors and critical exponents.

Contribution

It introduces a DMRG-based approach to compute eigenvalues related to current cumulants in non-equilibrium systems, providing new insights into phase transition behaviors.

Findings

Variance of current calculated in different phases

Scaling ansatz involving dynamical exponent z

Scaling properties of activity near absorbing state transition

Abstract

Cumulants of a fluctuating current can be obtained from a free energy-like generating function which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the DMRG for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process. Our results can be described in the terms of a scaling ansatz that involves the dynamical exponent z. We also calculate the generating function of the activity near the absorbing state transition of the contact process. Its scaling properties can be expressed in terms of known critical exponents.