Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion

Ruofei Yan, Hanshuang Chen

We study the fluctuation properties of the local time density, $\ddot{I}{}_T=\frac{1}{T}{\int }_0^T\hat{I}´(r(t)-1)dt$, spent by a $d$-dimensional Brownian particle at a spherical she…