Dynamical phase transition for current statistics in a simple driven diffusive system

TL;DR

This paper investigates a dynamical phase transition in a driven diffusive system, where the optimal density profile shifts from steady to time-dependent, leading to macroscopic jams that significantly alter current fluctuations.

Contribution

It provides a detailed analysis of the dynamical phase transition in current fluctuations, combining Monte Carlo simulations with macroscopic fluctuation theory predictions.

Findings

Identification of a critical current threshold for the phase transition

Observation of a traveling wave as the optimal density profile below the threshold

Excellent agreement between simulations and theoretical predictions

Abstract

We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time-dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly-correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, that hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large deviation function, but also the critical current threshold, the associated optimal density profiles and the traveling wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.