One-dimensional transport of interacting particles: Currents, density profiles, phase diagrams and symmetries

TL;DR

This paper investigates one-dimensional driven lattice gases with interactions, deriving exact current-density relations, analyzing boundary effects on phase diagrams, and exploring symmetries and mappings in non-equilibrium transport systems.

Contribution

It provides an exact current-density relation for interacting particles with Glauber rates and analyzes the impact of boundary conditions and symmetries on phase behavior.

Findings

Exact current-density relation derived for unidirectional hopping.

Boundary conditions significantly influence phase diagrams.

Particle-hole symmetry affects the topology of phase diagrams.

Abstract

Driven lattice gases serve as canonical models for investigating collective transport phenomena and properties of non-equilibrium steady states (NESS). Here we study one-dimensional transport with nearest-neighbor interactions both in closed bulk systems and in open channels coupled to two particle reservoirs at the ends of the channel. For the widely employed Glauber rates we derive an exact current-density relation in the bulk for unidirectional hopping. An approach based on time-dependent density functional theory provides a good description of the kinetics. For open systems, the system-reservoir couplings are shown to have a striking influence on boundary-induced phase diagrams. The role of particle-hole symmetry is discussed and its consequence on the topology of the phase diagrams. It is furthermore demonstrated that systems with weak bias can be mapped onto systems with unidirectional hopping.