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This study models boundary-induced nonequilibrium phase transitions using a particle exclusion process. Renormalization group analysis provides an analytical solution for particle density profiles, validated by numerical simulations.

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Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • The totally asymmetric simple exclusion process (TASEP) models boundary-induced nonequilibrium phase transitions.
  • In the continuum limit, particle density is governed by a singular differential equation with multiple scales, leading to boundary layers (BL) or shocks.

Purpose of the Study:

  • To develop a renormalization group (RG) analysis for the TASEP with adsorption and evaporation.
  • To obtain an analytical solution for the global particle density profile.
  • To validate the RG approach against numerical simulations.

Main Methods:

  • Renormalization group (RG) analysis applied to the TASEP.
  • Using boundary layer (BL) location and width as renormalization parameters.
  • Perturbative solution for BL and analytical derivation of the global density profile.

Main Results:

  • The RG analysis successfully cures large-distance divergences in the perturbative BL solution.
  • An analytical form for the global density profile is generated from the BL solution.
  • The predicted scaling form for the density profile is consistent with numerical solutions for finite systems.

Conclusions:

  • The developed RG method provides an effective analytical tool for studying TASEP with boundary-induced transitions.
  • The study offers a new perspective on understanding and predicting particle density profiles in nonequilibrium systems.
  • This work bridges theoretical modeling with numerical validation for complex physical phenomena.