Dynamical phase transitions in single particle Brownian motion without drift

TL;DR

This paper reveals that dynamical phase transitions can occur in single Brownian particles without drift, depending on system dimensionality, and links classical DPTs to quantum phase transitions.

Contribution

It demonstrates the existence of first- and second-order dynamical phase transitions in Brownian motion without drift, highlighting the role of dimensionality and quantum analogies.

Findings

First-order DPTs occur in dimensions higher than four.

Second-order DPTs with universal exponents are found in one-dimensional Brownian motion.

DPTs are associated with temporal phase separations and quantum phase transition analogies.

Abstract

Dynamical phase transitions (DPTs) arise from qualitative changes in the long-time behavior of stochastic trajectories, often observed in systems with kinetic constraints or driven out of equilibrium. Here we demonstrate that first-order DPTs can occur even in the large deviations of a single Brownian particle without drift, but only when the system's dimensionality exceeds four. These DPTs are accompanied by temporal phase separations in the trajectories and exhibit dimension-dependent order due to the threshold behavior for bound state formation in Schr\"{o}dinger operators. We also discover second-order DPTs in one-dimensional Brownian motion, characterized by universal exponents in the rate function of dynamical observables. Our results establish a novel framework linking classical DPTs to quantum phase transitions.