Occupation-time statistics of a gas of interacting diffusing particles

Tal Agranov, P. L. Krapivsky, and Baruch Meerson
Phys. Rev. E 99, 052102 – Published 2 May 2019

Abstract

The time that 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 noninteracting particles was addressed using the single-particle statistics. Here we employ the macroscopic fluctuation theory (MFT) to study the occupation-time statistics of many 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 noninteracting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.

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  • Received 1 January 2019

DOI:https://doi.org/10.1103/PhysRevE.99.052102

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Tal Agranov1,*, P. L. Krapivsky2,†, and Baruch Meerson1,‡

  • 1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
  • 2Department of Physics, Boston University, Boston, Massachusetts 02215, USA

  • *tal.agranov@mail.huji.ac.il
  • pkrapivsky@gmail.com
  • meerson@mail.huji.ac.il

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Issue

Vol. 99, Iss. 5 — May 2019

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