A minimal model of dynamical phase transition

TL;DR

This paper presents a simple model demonstrating a dynamical phase transition in a basic Markov process, characterized by non-analytic large deviation functions, without requiring complex scaling limits.

Contribution

It provides the first example of a dynamical phase transition in a homogeneous Markov process without additional scaling assumptions.

Findings

Large deviation functions exhibit non-analytic points.

Dynamical phase transition occurs in a simple, homogeneous Markov process.

No low-noise or large-volume limit needed for the transition.

Abstract

We calculate the large deviation functions characterizing the long-time fluctuations of the occupation of drifted Brownian motion and show that these functions have non-analytic points. This provides the first example of dynamical phase transition that appears in a simple, homogeneous Markov process without an additional low-noise, large-volume or hydrodynamic scaling limit.