A minimal model of dynamical phase 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.

v1: 5 pages, 2 figures; v2: minor corrections, close to published version

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• Occupation time statistics of a gas of interacting diffusing particles
• Varied phenomenology of models displaying dynamical large-deviation singularities
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival