On the phase transition in the sublattice TASEP with stochastic blockage

Abstract

We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process with local deterministic bulk dynamics and a stochastic defect that mimicks a random blockage. Exact results are obtained for the compressibility and density correlations for a stationary grandcanonical ensemble given by the matrix product ansatz. At the critical density the static compressibility diverges while in the phase separated state above the critical point the compressibility vanishes due to strong non-local correlations. These correlations arise from a long range effective interaction between particles that appears in the stationary state despite the locality of the microscopic dynamics.

Phase transitions in the driven lattice gas (TASEP) with repulsive energies

“…It should be noted that figure 15 provides a generic picture which seems to be valid for other cases of α and β in the P αβ regime close to ε c1 . It is generally believed and it has been shown that shocks can perform random walks along the x-axis [42,43,45]. At the microscopic level the structure, location and diffusion of a shock can be examined by simulations quite accurately and is discussed in the following.…”

“…a discontinuity in the density profile which can perform random walks along the x-axis. The phenomenon of phase separation in equilibrium systems has its non-equilibrium analog in models of the driven lattice gas [42][43][44][45].…”

Defect-induced anticorrelations in molecular motor traffic

“…For self-containedness we recall the precise definition of the process and some of its basic stationary properties which were proved in [33,57,58,63] and used extensively in this work.…”

“…As shown in [57], the matrix product ansatz of [63] can conveniently be reformulated in terms of two-dimensional unit matrix 𝟙 and the matrices…”

“…In this work we study correlations between translocation at some binding site and the presence of motors on some other-possibly far distant-binding site. In particular, we discuss (i) the emergence of anticorrelations that have been discovered recently also for the particle density [57,58] and (ii) how the phase transition is reflected in the velocity of kinematic density waves that arise as a collective phenomenon from local density perturbations [17,[59][60][61][62].…”