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Semi-infinite Simple Exclusion Process: From Current Fluctuations to Target Survival
Aurélien Grabsch1, Hiroki Moriya1, Kirone Mallick2
1<a href="https://ror.org/02en5vm52">Sorbonne Université</a>, CNRS, <a href="https://ror.org/04zaaa143">Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)</a>, 4 Place Jussieu, 75005 Paris, France.
Physical Review Letters
|September 27, 2024
Summary
We derived the current statistics for the symmetric simple exclusion process (SEP) in a semi-infinite system. This advances understanding of particle transport and solves open problems in target survival and source injection.
Area of Science:
- Statistical Mechanics
- Many-Body Physics
- Transport Phenomena
Background:
- The symmetric simple exclusion process (SEP) models particle transport in single-file systems.
- Existing studies focus on finite or infinite systems, leaving intermediate cases less explored.
Purpose of the Study:
- To derive the cumulant generating function for integrated current in a semi-infinite SEP.
- To address limitations of previous studies by analyzing a system that doesn't conserve particles or reach a steady state.
Main Methods:
- Determining the full spatial structure of correlations.
- Inferring and applying a closed equation for correlations, previously found for infinite systems.
Main Results:
- Obtained an expression for the full cumulant generating function of the integrated current.
- Established the exactness of the correlation structure equation for the semi-infinite geometry.
- Solved open problems regarding target survival probability and particle source statistics.
Conclusions:
- The derived results provide a comprehensive understanding of transport in semi-infinite SEP systems.
- This work bridges the gap between finite and infinite system analyses.
- The findings have implications for statistical mechanics and related fields.
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