Dynamical phase transitions in two-dimensional Brownian Matter

TL;DR

This paper explores the collective dynamics and phase transitions of two-dimensional Brownian particles, revealing a gauge symmetry and multiple dynamical regimes through a field-theoretic approach.

Contribution

It introduces a novel gauge theory framework for describing density fluctuations in 2D Brownian matter and uncovers dynamical phase transitions in the system.

Findings

Identification of an exact symmetry under area-preserving diffeomorphisms.

Emergence of a U(1) gauge symmetry in the density fluctuation dynamics.

Presence of multiple dynamical regimes and phase transitions even with purely repulsive interactions.

Abstract

We investigate collective behavior of a system of two-dimensional interacting Brownian particles in the hydrodynamic regime. By means of the Martin-Siggia-Rose-Jenssen-de Dominicis formalism, we built up a generating functional for correlations functions. In the continuum limit, we uncover an exact symmetry under area-preserving diffeomorphism transformations that characterizes a liquid state. This symmetry leads to the conservation of local vorticity. By computing the generating functional within the saddle-point plus Gaussian fluctuations approximation, we reveal the emergence of a $U(1)$ gauge symmetry that allows us to describe the dynamics of density fluctuations as a gauge theory. We solve the corresponding equations of motion for short as well as long ranged interactions showing up the presence of multiple dynamical regimes and associated dynamical phase transitions, even for pure repulsive interactions.