Dynamics of Driven Diffusive Systems with Interactions and with Langmuir kinetics

Driven diffusive system belongs to a special class of nonequilibrium systems that has wide applications in biological and vehicular transport processes. During intracellular transport of vesicles along microtubules, motor proteins interact among each other as well as frequently associate and dissociate from the tracks. Motivated by the above phenomenon, we develop a model that assimilates the interactions along with the nonconserved Langmuir kinetics in a totally asymmetric simple exclusion process [1]. We find that the continuum version of the simple mean-field (SMF) approach fails to handle strong correlations in the system. To incorporate the effect of correlation, we analyze the model using the correlated cluster mean-field theory. We compute the stationary phase diagrams, density, current and correlation profiles along the lattice for the various strength of attractive and repulsive interaction energy. Our results are in excellent agreement with the Monte Carlo computer simulations. For the case of attractions, we find the two-point correlation function to be stronger at the position of localized shocks.


References
[1] Tripti Midha, Anatoly B. Kolomeisky, and Arvind Kumar Gupta, "Interactions in nonconserving driven diffusive systems" Phys. Rev. E 98, 042119.