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Generalized Correlation Profiles in Single-File Systems.

Alexis Poncet1,2, Aurélien Grabsch1, Pierre Illien3

  • 1Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France.

Physical Review Letters
|December 10, 2021
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Summary
This summary is machine-generated.

Generalized correlation profiles (GCPs) in single-file diffusion reveal non-monotonic spatial dependence, offering a complete description of tracer and bath particle correlations beyond tracer-only models.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Many-Body Systems

Background:

  • Single-file diffusion describes particle motion in confined spaces where particles cannot overtake.
  • Existing models primarily focus on tracer particle behavior, neglecting bath particle correlations.
  • Understanding these correlations is crucial for a complete description of the system.

Purpose of the Study:

  • To introduce and analytically derive Generalized Correlation Profiles (GCPs) for single-file diffusion.
  • To characterize the correlations between tracer position and bath particle density.
  • To extend beyond tracer-only descriptions in many-body diffusion problems.

Main Methods:

  • Development of an analytical framework for GCPs within the tracer's reference frame.
  • Analysis in the hydrodynamic limit to determine scaling forms of GCPs.
  • Exact results derived for paradigmatic single-file diffusion models.

Main Results:

  • GCPs fully characterize tracer-bath particle correlations.
  • A non-monotonic spatial dependence of GCPs was discovered, even without system asymmetry.
  • Analytical solutions for GCPs were obtained for Brownian particles, symmetric exclusion, and random average processes.

Conclusions:

  • The introduced GCPs provide a comprehensive description of single-file diffusion systems.
  • The findings reveal unexpected spatial correlations in a seemingly symmetric system.
  • The analytical approach is versatile, applicable to various interactions and non-equilibrium conditions.