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arXiv · 1901.00153

Occupation time statistics of a gas of interacting diffusing particles

Tal Agranov·P. L. Krapivsky·Baruch Meerson
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Abstract

The time which a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently the joint occupation time statistics of an ensemble of non-interacting particles was addressed using the single-particle statistics. Here we employ the Macroscopic Fluctuation Theory (MFT) to study the occupation time statistics of many \emph{interacting} particles. We find that interactions can significantly change the statistics and, in some models, even cause a singularity of the large-deviation function describing these statistics. This singularity can be interpreted as a dynamical phase transition. We also point out to a close relation between the MFT description of the occupation-time statistics of non-interacting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.

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Tal Agranov, P. L. Krapivsky, Baruch Meerson. 2019-04-07. Occupation time statistics of a gas of interacting diffusing particles. https://doi.org/10.1103/physreve.99.052102

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