Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems

TL;DR

This paper investigates how biased ensembles of trajectories in diffusive systems can lead to phase transitions into hyperuniform states, characterized by suppressed large-scale density fluctuations, using fluctuating hydrodynamics and numerical simulations.

Contribution

It demonstrates that biased diffusive systems undergo phase transitions into hyperuniform states and analyzes their behavior using fluctuating hydrodynamics and numerical models.

Findings

Biased ensembles exhibit phase transitions into hyperuniform states.

Large-wavelength density fluctuations are strongly suppressed in these states.

Homogeneous states with normal fluctuations only occur under very weak bias.

Abstract

We analyse biased ensembles of trajectories for diffusive systems. In trajectories biased either by the total activity or the total current, we use fluctuating hydrodynamics to show that these systems exhibit phase transtions into `hyperuniform' states, where large-wavelength density fluctuations are strongly suppressed. We illustrate this behaviour numerically for a system of hard particles in one dimension and we discuss how it appears in simple exclusion processes. We argue that these diffusive systems generically respond very strongly to any non-zero bias, so that homogeneous states with "normal" fluctuations (finite compressibility) exist only when the bias is very weak.