Speaker
Description
The study of the dynamics of occupation time has a variety of applications. For ex-
ample, it has been used to analyze the morphological dynamics of interfaces, analysis
of the fluorescence intermittency emitting from colloidal semiconductor dots, optical
imaging etc to name a few. The occupation time dynamics have been studied for
numerous problems in the context of non-equilibrium systems. In this work we study
the large deviation statistics of occupation fraction of N non-crossing Brownian par-
ticles in a certain interval. Using the extension of the Donsker-Varadhan formalism
we solve this problem by mapping it to N non-interacting spinless fermions trapped
in a square well potential. We study the behaviour of the large deviation function for
all N ≥ 1. For N = 1, the single Brownian motion in presence of a drift is known to
exhibit dynamical phase transition of first order where the large deviation function
shows singularity. For any N ≥ 2, we interestingly find that the system undergoes
multiple dynamical phase transitions of second order. This phenomenon is entirely
different from what is found for a single Brownian motion occupation fraction. Here
each transition denotes different numbers of particle occupations near the vicinity of
the interval.
