Nonequilibrium processes: driven lattice gases, interface dynamics, and quenched-disorder effects on density profiles...

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Complex Systems

Background:

• The one-dimensional totally asymmetric simple exclusion process (TASEP) is a fundamental model for studying driven systems and interface dynamics.
• Understanding the connection between TASEP properties and the Kardar-Parisi-Zhang (KPZ) equation is crucial for characterizing dynamical scaling in various physical systems.
• Previous studies have explored TASEP with different boundary conditions, but discrepancies with theoretical predictions, particularly from Bethe ansatz, persist in certain phases.

Purpose of the Study:

• To investigate the properties of TASEP and their relationship with the dynamical scaling of moving interfaces described by the KPZ equation.
• To determine the scaling exponents (alpha, z, beta) under periodic and open boundary conditions, and for TASEP with quenched disorder.
• To reconcile discrepancies between simulation results and Bethe ansatz predictions in the low-density phase of TASEP.

Main Methods:

• Numerical simulations of TASEP with periodic and open boundary conditions.
• Analysis of interface width scaling using a discrete occupation-number-to-height mapping.
• Mean-field continuum formulation to analyze relaxation times and kinematic-wave propagation.
• Direct analytic approach to steady-state properties of TASEP with quenched disorder.

Main Results:

• Under periodic boundary conditions, interface width scaling yields exponents alpha=0.500(5), z=1.52(3), beta=0.33(1).
• With open boundaries, the maximal-current phase exhibits exponents consistent with periodic cases and Bethe ansatz predictions.
• In the low-density phase, exponents alpha=0.497(3), z=1.20(5), beta=0.41(2) were found, differing from the Bethe ansatz prediction z=0; a mean-field analysis suggests a characteristic relaxation time with z=1 explains this discrepancy.
• On the coexistence line, alpha=0.99(1), z=2.10(5), beta=0.47(2) agree well with Bethe ansatz predictions (z=2).
• For TASEP with quenched disorder, interface width scaling gives alpha=1.05(5), z=1.7(1), beta=0.62(7), and analytic methods provide density profiles and current bounds.

Conclusions:

• The study clarifies the dynamical scaling behavior of TASEP interfaces under various conditions, resolving discrepancies with theoretical predictions.
• A mean-field approach successfully explains the observed scaling in the low-density phase of open-boundary TASEP.
• TASEP with quenched disorder exhibits distinct scaling properties, with analytical results providing a deeper understanding of its steady-state characteristics.