Boundary-drive–induced formation of aggregate condensates in stochastic transport with short-range interactions

Abstract

-We discuss the effects of particle exchange through open boundaries and the induced drive on the phase structure and condensation phenomena of a stochastic transport process with tunable short-range interactions featuring pair-factorized steady states (PFSS) in the closed system. In this model, the steady state of the particle hopping process can be tuned to yield properties from the zero-range process (ZRP) condensation model to those of models with spatially extended condensates. By varying the particle exchange rates as well as the presence of a global drift, we observe a phase transition from a free particle gas to a phase with condensates aggregated to the boundaries. While this transition is similar to previous results for the ZRP, we find that the mechanism is different as the presence of the boundary actually influences the interaction due to the non-zero interaction range.Condensation phenomena are observed in a broad range of physical processes. While they are originally associated with phase transitions of matter from the gas state to some liquid or solid state, they are also closely related to nucleation and coarsening phenomena. Examples of condensation appear in processes such as the formation of breath figures [1], Bose-Einstein condensation [2], polymer aggregation [3], but in a wider sense also in more generic systems like networks as the formation of clusters [4] through the accumulation of links on sites.For many such systems, the involved condensation process can be modeled as a stochastic transport process with a set of particles occupying a number of discrete sites. With particles representing microscopic to macroscopic objects and appropriate dynamics a wide spectrum of physical processes has been studied. Examples include refs. [2, 4] mentioned above, but also processes such as wealth condensation [5] or traffic flow [6].The zero-range process (ZRP) with condensation dynamics [7,8] is a well known paradigm of such transport processes. While it has a fully symmetric steady state, above some critical density ρ c the symmetry breaks spon-(a) E-mail: hannes.nagel@itp.uni-leipzig.de (b) E-mail: h.ortmanns@jacobs-university.de (c) E-mail: wolfhard.janke@itp.uni-leipzig.de taneously and a particle condensate emerges at a single site such that the density at the remaining sites stays critical. When short-range interactions are introduced, a similar condensation process can be observed with the main difference, that condensates can be spatially extended [9][10][11][12]. In this work, however, we shall consider condensation not as an effect in the steady state, but as a signature of a boundary induced phase transition. Such transitions can occur in driven systems, where the drive is implemented in terms of the interaction at the boundary of the system [13]. A well known transport process with such a transition is the totally asymmetric simple exclusion process (TASEP) [14,15], where a high-density, a lowdensity and a maximal-current phase exist [16]. For the ZRP, such effects of open boun...

Emergence of dynamic phases in the presence of different kinds of open boundaries in stochastic transport with short-range interactions

“…We did, however, consider only one specific type of open boundaries and were severely limited by the employed numerical method. In a recent short communication [25], we sketched an improved simulation setup and discussed for this special case the phase diagram and transition dynamics between the phases in more detail. In particular, we pointed out that not only the details but, in fact, the very existence of phases depends on the choice of interaction with the boundary.…”

Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales

“…In this model, the stationary state factorizes over lattice bonds instead of sites as for the ZRP, which is why it is often referred to as the pair-factorized steady states (PFSS) model, mainly to distinguish from the fully factorized steady state of the ZRP. Many stationary properties of the condensed state in this family of models such as the condensate's shape and length scale [22][23][24], mobility [25,26], metastability of the condensate [27] or boundary induced phase separation [28][29][30] were studied.…”