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Occupation-time statistics of a gas of interacting diffusing particles
Tal Agranov1, P L Krapivsky2, Baruch Meerson1
1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Interacting particles exhibit altered occupation-time statistics, potentially leading to dynamical phase transitions. Macroscopic fluctuation theory reveals insights into these complex behaviors.
Area of Science:
- Statistical Mechanics
- Many-Body Physics
- Dynamical Systems
Background:
- Occupation time, or residence time, quantifies particle dwell time in a specific spatial region.
- Previous studies analyzed joint occupation-time statistics for noninteracting particles using single-particle statistics.
Purpose of the Study:
- To investigate the occupation-time statistics of interacting particles using macroscopic fluctuation theory (MFT).
- To understand how inter-particle interactions influence statistical properties and potentially induce phase transitions.
Main Methods:
- Application of Macroscopic Fluctuation Theory (MFT) to a system of interacting particles.
- Analysis of large-deviation functions to characterize occupation-time statistics.
Main Results:
- Particle interactions significantly modify occupation-time statistics.
- In certain models, interactions induce singularities in the large-deviation function, interpretable as dynamical phase transitions.
- A connection is established between MFT for noninteracting particles and the level 2 large deviation formalism for single-particle occupation times.
Conclusions:
- Interactions introduce novel phenomena in occupation-time statistics, including dynamical phase transitions.
- MFT provides a powerful framework for studying these complex statistical behaviors in interacting systems.
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