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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.

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|September 27, 2024
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Summary
This summary is machine-generated.

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.

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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.