Role of interactions in a closed quenched driven diffusive system

Abstract

We study the non-equilibrium steady states in a closed system consisting of interacting particles obeying exclusion principle with quenched hopping rate. Cluster mean field approach is utilized to theoretically analyze the system dynamics in terms of phase diagram, density profiles, current, etc, with respect to interaction energy E. It turns out that on increasing the interaction energy beyond a critical value, E c, shock region shows non-monotonic behavior and contracts until another critical value E c 1 is attained; a further increase leads to its expansion. Moreover, the phase diagram of an interacting system with specific set of parameters has a good agreement with its non-interacting analogue. For interaction energy below E c, a new shock phase displaying features different from non-interacting version is observed leading to two distinct shock phases. We have also performed Monte Carlo simulations extensively to validate our theoretical findings.

Interaction vs inhomogeneity in a periodic TASEP

“…The presence of three different regimes is revealed, as the repulsion strength increases (see figure 1). In case of weak repulsion (figure 1(a)), the behaviour of the system is qualitatively equivalent to that of a system without NN interaction [16], with a single phase at intermediate densities, characterized by the presence of a shock in the density profile and maximal current (S MC phase), and by Three regimes observed in [40], as a function of the (mean) particle density: (a) no interaction or weak interaction; (b) mildly strong interaction; (c) very strong interaction. Phase tags are explained in the text.…”

“…The PA theory will be first developed in such a general case. Subsequently, we shall take some more restrictive hypotheses, along the lines of [40] and previous literature [29-32, 38, 39]. In particular, we shall assume the following expressions for the rates, whose meaning is discussed below 5 :…”

“…We shall also introduce some restrictive hypotheses on the p, q, r, s parameters. As in Pal and Gupta's work [40], we shall first assume p = s, which turns out to induce a particle-hole symmetry 6 . In fact, one of the four parameters can be set equal to 1 without loss of generality, so the imposed condition will actually be…”

“…Still motivated by biological transport phenomena, as well as by methodological issues, [38] investigates the role of NN interactions in a TASEP with Langmuir kinetics, though without inhomogeneities. Furthermore, [39,40] investigate the interplay between NN interactions and rate inhomogeneities, in the presence of open [39] or periodic [40] boundary conditions. In particular, the recent work by Pal and Gupta [40] (periodic boundary conditions) points out that a NN repulsive interaction, in combination with a very simple rate inhomogeneity (represented by a regular function with a single minimum and a single maximum) gives rise to a seemingly non-trivial phenomenology.…”

“…Furthermore, [39,40] investigate the interplay between NN interactions and rate inhomogeneities, in the presence of open [39] or periodic [40] boundary conditions. In particular, the recent work by Pal and Gupta [40] (periodic boundary conditions) points out that a NN repulsive interaction, in combination with a very simple rate inhomogeneity (represented by a regular function with a single minimum and a single maximum) gives rise to a seemingly non-trivial phenomenology. The presence of three different regimes is revealed, as the repulsion strength increases (see figure 1).…”