Eur. Phys. J. B (2016) 89: 135
https://doi.org/10.1140/epjb/e2016-70192-5

Regular Article

Totally asymmetric simple exclusion process on a periodic lattice with Langmuir kinetics depending on the occupancy of the forward neighboring site

¹ Department of Advanced Interdisciplinary Studies, Graduate School of Engineering, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, 153-8904 Tokyo, Japan
² Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, 153-8904 Tokyo, Japan
³ Department of Aeronautics and Astronautics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-8656 Tokyo, Japan

^a e-mail: ichiki@jamology.rcast.u-tokyo.ac.jp

Received: 22 February 2016
Received in final form: 27 March 2016
Published online: 25 May 2016

Abstract

We generalize the totally asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. In the extended model, the rates of attachment and detachment depend on the occupancy of the forward neighboring site. Using a mean-field theory, we obtain the analytical expression of the density profile in the steady state and the relaxation dynamics in our model. We verify their accuracy by comparing the results with Monte Carlo simulations.