Integrable Boundary Conditions in Asymmetric Diffusion Processes

TL;DR

This paper explores exactly solvable asymmetric diffusion processes with open boundaries, analyzing stationary states, boundary conditions, and phase classification using a recursion formula.

Contribution

It introduces an equation with an auxiliary parameter to determine boundary conditions for exact solvability in asymmetric diffusion models.

Findings

Classified phases based on density current and concentration

Derived an equation to identify boundary conditions for solvability

Analyzed stationary states with nonlocal open boundaries

Abstract

We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be determined in an elementary way. We give the equation which includes an auxiliary parameter and determines possible boundary conditions for the model to be solved exactly. With the help of that equation, we analyze the density current and concentration. We classify the phases according to them.