Universality in the dynamical phase transitions of Brownian motion

TL;DR

This paper investigates dynamical phase transitions in Brownian motion, revealing that both first- and second-order DPTs occur in various dimensions and configurations, with implications for understanding trajectory localization and phase behavior.

Contribution

It demonstrates the presence of first- and second-order dynamical phase transitions in Brownian motion across different dimensions and particle numbers, extending previous understanding.

Findings

First-order DPTs occur in high-dimensional Brownian motion.

Second-order DPTs are linked to trajectory localization in 1D.

DPTs are observable in many-particle systems at lower dimensions.

Abstract

We study the dynamical phase transitions (DPTs) appearing for a single Brownian particle without drift. We first explore how first-order DPTs in large deviations can be found even for a single Brownian particle without any force upon raising the dimension to higher than four. The DPTs accompany temporal phase separations in their dynamical paths, which we numerically confirm by fitting to scaling functions. We next investigate how second-order DPTs can appear in one-dimensional free Brownian motion by choosing the observable, which essentially captures the localization transition of the trajectories. We discuss and confirm that the DPTs predicted for high dimensions can also be found when considering many Brownian particles at lower dimensions.