Relaxation dynamics of closed diffusive systems with infinitesimal Langmuir kinetics

TL;DR

This paper analytically investigates the relaxation dynamics of a closed diffusive system with infinitesimal Langmuir kinetics, deriving exact stationary and excited states, and proposing formulas for the system's time evolution.

Contribution

It provides the first analytical derivation of stationary and excited states for the closed asymmetric exclusion process with infinitesimal Langmuir kinetics.

Findings

Exact stationary state obtained

Series of excited states derived

Analytical formulas for time evolution proposed

Abstract

We consider the asymmetric simple exclusion process with Langmuir kinetics in the closed boundary condition. We analytically obtain the exact stationary state and a series of excited states of the system in the limit where Langmuir kinetics is infinitesimally small. Based on this result, we propose an analytical formula for the time evolutions of physical quantities of the system.