Coupling driven exclusion and diffusion processes on parallel lanes: boundary induced phase transitions and boundary layers

摘要

We study a driven many particle system comprising of two identical lanes offinite lengths. On one lane, particles hop diffusively with a bias in aspecific direction. On the other lane, particles hop in a specific directionobeying mutual exclusion rule. In addition, the two lanes are connected witheach other through exchange of particles with certain rules. The system, at itstwo ends, is in contact with particle reservoirs which maintain specificparticle densities at the two ends. In this paper, we study boundary-inducedphase transitions exhibited by this system and predict the phase diagram usingthe technique of fixed point based boundary layer analysis. An interestingmanifestation of the interplay of two density variables associated with twolanes is found in the shock phase in which the particle density profile acrossthe lane with unidirectional hopping shows a jump discontinuity (shock) from alow- to a high-density region. The density profile on the diffusion-lane neverexhibits a shock. However, the shock in the other lane gives rise to adiscontinuity in the slope of the diffusion-lane density profile. We show howan approximate solution for the slope can be obtained in the boundary layeranalysis framework.