Dynamical phase transitions in single particle Brownian motion without drift

Takahiro Kanazawa; Kyogo Kawaguchi; Kyosuke Adachi

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arXiv · 2407.18282

Dynamical phase transitions in single particle Brownian motion without drift

Takahiro Kanazawa·Kyogo Kawaguchi·Kyosuke Adachi

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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.

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Takahiro Kanazawa, Kyogo Kawaguchi, Kyosuke Adachi. 2024-07-25. Dynamical phase transitions in single particle Brownian motion without drift. https://arxiv.org/abs/2407.18282

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