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We explored driven tracer dynamics in the symmetric exclusion process (SEP), a model for anomalous diffusion. Our new hydrodynamic framework reveals the bias dependence of tracer variance for any density, advancing nonequilibrium transport understanding.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Nonlinear Dynamics

Background:

  • The symmetric exclusion process (SEP) models anomalous diffusion with hard-core particles on a lattice.
  • Driven tracer dynamics in SEP under external force is crucial for understanding nonequilibrium transport but remains underexplored.
  • Existing analytical results are limited to mean values and high-density approximations.

Purpose of the Study:

  • To develop a general hydrodynamic framework for driven tracer dynamics in SEP.
  • To determine cumulants of tracer position and bath-tracer correlations beyond linear response.
  • To analyze the bias dependence of tracer variance at arbitrary densities.

Main Methods:

  • Development of a general hydrodynamic framework.
  • Calculation of first cumulants of bath-tracer correlations.
  • Derivation of tracer position cumulants up to quadratic order in the driving force.

Main Results:

  • The study provides the first determination of the bias dependence of the variance for a driven tracer in SEP across all densities.
  • Analytical results for tracer position and bath-tracer correlations are derived up to quadratic order.
  • The framework allows for the calculation of higher-order moments beyond linear response.

Conclusions:

  • The developed hydrodynamic framework offers a comprehensive approach to driven tracer dynamics in SEP.
  • This work significantly advances the understanding of nonequilibrium transport in crowded environments.
  • The methodology is applicable to broader systems involving driven tracers interacting with obstacles in one dimension.