Relaxation dynamics of the asymmetric simple exclusion process with Langmuir kinetics on a ring

TL;DR

This paper analytically studies the relaxation dynamics of the ASEP with Langmuir kinetics on a ring, deriving exact time evolution, stationary states, and relaxation times, including for partially asymmetric cases.

Contribution

It introduces a basis transformation that simplifies proofs of stationarity and extends analysis to partially asymmetric models, providing exact relaxation times.

Findings

Exact time evolution of correlation functions derived

Stationary state proven for the partially asymmetric case

Exact relaxation times obtained

Abstract

We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no particle in the system. The exact stationary state of this model has been known for the totally asymmetric case. We propose a basis transformation which simplifies the proof of the stationarity of this state and enables the generalization to the partially asymmetric case. Moreover, we construct low-energy excitations and obtain the exact relaxation time.