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Published on: August 21, 2018
Asymmetric simple exclusion process with periodic boundary driving.
Vladislav Popkov1, Mario Salerno, Gunter M Schütz
1Dipartimento di Fisica ER Caianiello, and Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, Università di Salerno, Baronissi, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
The asymmetric simple exclusion process (ASEP) on a semi-infinite chain develops a periodic sawtooth density profile. This behavior is independent of initial conditions and analytically derived in the hydrodynamic limit.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Systems
- Condensed Matter Physics
Background:
- The asymmetric simple exclusion process (ASEP) is a fundamental model for driven diffusive systems.
- Understanding particle transport in systems with time-dependent boundary conditions is crucial.
Purpose of the Study:
- To analyze the behavior of the ASEP on a semi-infinite chain coupled to a time-periodic reservoir.
- To determine the emergent density profile and stationary state properties.
Main Methods:
- Analytical derivation in the hydrodynamic limit.
- Numerical determination of effective boundary densities using Monte Carlo simulations.
- Comparison with mean-field and Burgers equation solutions.
Main Results:
- A time-periodic sawtooth-like density profile emerges, independent of initial conditions.
- The stationary state in finite systems is governed by effective boundary densities and the extremal flux principle.
- Numerical results for effective boundary densities align with analytical predictions and numerical integrations.
Conclusions:
- The study provides an analytical solution for the ASEP with time-periodic boundary conditions.
- The findings are generalizable to other driven diffusive systems with conserved particle species.
- Effective boundary densities play a key role in determining the stationary state of finite systems.
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