Stochastic systems with Bose-Hubbard interactions: Effects of bias on particles on a 1D lattice

TL;DR

This paper studies a 1D lattice model with Bose-Hubbard interactions under bias, revealing how drive, interactions, and boundaries influence steady-state correlations, currents, and density profiles.

Contribution

It introduces a stochastic 1D lattice model with Bose-Hubbard interactions and bias, analyzing steady-state properties under different boundary conditions.

Findings

Non-monotonic correlation dependence on interaction strength

Emergence of ASEP-like states at high interactions

Step-like density profiles under open boundaries

Abstract

Driven non-equilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional lattice system that allows multiple particle occupancy on each site. The particles undergo stochastic nearest-neighbor jumps influenced by both a directional bias and on-site repulsive interactions of the Bose-Hubbard type. With periodic boundary conditions, we observe a non-monotonic dependence of inter-site correlation functions on the interaction strength. At large interaction strengths, the state consists of quiescent stacks of stationary particles along with an emergent asymmetric simple exclusion process(ASEP), and the particle current exhibits a periodic dependence on density. In contrast, with open boundary conditions, the system displays step-like density profiles reminiscent of those in tilted Bose-Hubbard systems, and a regime with a macroscopic number of empty sites followed by a steep parameter-dependent increase in density. Our results highlight how the interplay between drive, interaction, and boundary conditions leads to distinctive signatures on the current and density profiles in the steady state in different regimes.