Global Density Profile For Particle Non-Conserving One Dimensional Transport From Renormalization Group Flows

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.