Minimal current phase and universal boundary layers in driven diffusive systems

Abstract

We investigate boundary-driven phase transitions in open driven diffusive systems. The generic phase diagram for systems with short-ranged interactions is governed by a simple extremal principle for the macroscopic current, which results from an interplay of density fluctuations with the motion of shocks. In systems with more than one extremum in the current-density relation, one finds a minimal current phase even though the boundaries support a higher current. The boundary layers of the critical minimal current and maximal current phases are argued to be of a universal form. The predictions of the theory are confirmed by Monte Carlo simulations of the two-parameter family of stochastic particle hopping models of Katz, Lebowitz, and Spohn and by analytical results for a related cellular automaton with deterministic bulk dynamics. The effect of disorder in the particle jump rates on the boundary layer profile is also discussed.

Large Deviation Functional of the Weakly Asymmetric Exclusion Process

“…in agreement with [18,30], and that K λ (ρ a , ρ b ) ≃ log J in (2.4) so that (2.10) reduces to (1.6). …”

Multishocks in driven diffusive processes: Insights from fixed-point analysis of the boundary layers

“…Double peak structure of the current-density relation leads to two maximum current and one minimum cur-rent phases in the phase diagram of the particle conserving repulsion model [3]. In the maximum and minimum current phases, the bulk density values are those at which the current attains its maximum and minimum values respectively.…”

“…For ǫ = 0, there is an effective repulsion between the particles [2,3,9]. In addition, the number of particles is not conserved due to particle detachment, 1 → 0, at a rate ω d and attachment, 0 → 1, at a rate ω a at any site on the lattice.…”

“…The current, therefore, vanishes exactly at the half-filling (ρ = 1/2) with the maximum current appearing symmetrically for densities on the two sides of ρ = 1/2. The exact form of the current as a function of ρ for arbitrary ǫ can be found using a transfer matrix approach [3] and it evolves from a single to a symmetric double peak structure as ǫ grows beyond ǫ J ≈ .8. A simple, analytically tractable form of the current with double peaks can be obtained by doing a double expansion of the exact current about ǫ = ǫ J and ρ = 1/2 [11].…”

“…There exist other models where particles can have attractive or repulsive interaction in addition to the exclusion interaction [2,3].…”