Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion
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arXiv
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| Format: | Preprint |
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2025
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| author | Yan, Ruofei Chen, Hanshuang |
| author_facet | Yan, Ruofei Chen, Hanshuang |
| contents | We study the fluctuation properties of the local time density, ${ρ_T} = \frac{1}{T}\int_0^T {δ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial distance from the particle to the origin. In the large observation time limit, $T \to \infty$, the local time density $ρ_T$ obeys the large deviation principle, $P(ρ_T= ρ) \sim e^{-T I(ρ)}$, where the rate function $I(ρ)$ is analytic everywhere for $d\leq 4$. In contrast, for $d>4$, $I(ρ)$ becomes nonanalytic at a specific point $ρ=ρ_c^{(d)}$, where $ρ_c^{(d)}=d(d-4)/(2d-4)$ depends solely on dimensionality. The singularity signals the occurrence of a first-order dynamical phase transition in dimensions higher than four. Such a transition is accompanied by temporal phase separations in the large deviations of Brownian trajectories. Finally, we validate our theoretical results using a rare-event simulation approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion Yan, Ruofei Chen, Hanshuang Statistical Mechanics We study the fluctuation properties of the local time density, ${ρ_T} = \frac{1}{T}\int_0^T {δ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial distance from the particle to the origin. In the large observation time limit, $T \to \infty$, the local time density $ρ_T$ obeys the large deviation principle, $P(ρ_T= ρ) \sim e^{-T I(ρ)}$, where the rate function $I(ρ)$ is analytic everywhere for $d\leq 4$. In contrast, for $d>4$, $I(ρ)$ becomes nonanalytic at a specific point $ρ=ρ_c^{(d)}$, where $ρ_c^{(d)}=d(d-4)/(2d-4)$ depends solely on dimensionality. The singularity signals the occurrence of a first-order dynamical phase transition in dimensions higher than four. Such a transition is accompanied by temporal phase separations in the large deviations of Brownian trajectories. Finally, we validate our theoretical results using a rare-event simulation approach. |
| title | Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2508.05956 |