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Large deviations in single-file diffusion.

P L Krapivsky1, Kirone Mallick2, Tridib Sadhu2

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We studied tracer diffusion in single-file systems using macroscopic fluctuation theory. The tracer

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Single-file diffusion describes particle movement where particles cannot overtake each other.
  • Understanding tracer diffusion is crucial for various physical and biological systems.

Purpose of the Study:

  • To investigate tracer diffusion in one-dimensional interacting particle systems.
  • To apply macroscopic fluctuation theory to analyze single-file diffusion dynamics.

Main Methods:

  • Macroscopic fluctuation theory was employed.
  • Cumulant generating function and large deviation function were derived for Brownian particles with hard-core repulsion.
  • Tracer position variance was expressed using collective transport properties for general interactions.

Main Results:

  • Derived the cumulant generating function and large deviation function for tracer position in a specific single-file system.
  • Expressed tracer position variance in terms of diffusion coefficient and mobility for general interparticle interactions.
  • The analysis holds for both annealed and quenched initial configurations.

Conclusions:

  • Macroscopic fluctuation theory provides a powerful framework for studying single-file diffusion.
  • Collective transport properties govern tracer diffusion in these systems.
  • The findings are applicable to systems with both fluctuating and fixed initial states.