Totally asymmetric simple exclusion process with Langmuir kinetics

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Non-equilibrium Systems

Background:

• Investigates a driven lattice gas model by combining the totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics.
• Focuses on systems where these competing dynamics lead to nonconserved particle flow.

Purpose of the Study:

• To analyze the emergent stationary regimes and phase behavior in a driven lattice gas under competing dynamics.
• To explain unexpected phenomena like localized domain walls and phase coexistence.
• To develop a theoretical framework for understanding the system's critical properties and scaling behavior.

Main Methods:

• Coupling of one-dimensional totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics.
• Numerical simulations to observe particle density and current profiles.
• Mean-field analysis in the continuum limit, utilizing Lambert W functions for analytic solutions.

Main Results:

• Observation of localized domain walls separating low and high particle density regions (phase coexistence).
• Discovery of a rich phase diagram including high/low density phases, multi-phase coexistence, and a boundary-independent 'Meissner' phase.
• Analytic solution derived using Lambert W functions accurately describes phase diagram and critical exponents of domain walls.

Conclusions:

• The mean-field approach successfully rationalizes simulation results and explains the domain wall localization phenomenon.
• Unusual mean-field exponents characterizing domain wall critical properties were extracted.
• The study provides insights into phenomena beyond mean-field, including domain wall scaling properties.