Driven diffusive systems with disorder

Abstract

We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial distribution of transition rates, both with a single easy direction and with random reversals of the easy direction; dynamical disorder, where particles move in a disordered landscape which itself evolves in time. In every case, the system exhibits phase separation; in some cases, it is of an unusual sort. The time-dependent properties of density fluctuations are in accord with the kinematic wave criterion that the dynamical universality class is unaffected by disorder if the kinematic wave velocity is nonzero.

Mean-field treatment of exclusion processes with random-force disorder

“…For this paradigmatic model of driven interacting particle systems many exact results are available [7]. As most of the real systems are not ideally translationally invariant, for instance the filaments on which molecular motors move are heterogeneous, a challenging problem is the study of spatially inhomogeneous versions of exclusion processes [8,9,10,11,12,13,14,15,16,17,18] for which the bulk of results is obtained by phenomenological methods based on the statistics of extremes, by mean field approximation and by Monte Carlo simulations. Most works concern the onedimensional totally asymmetric process where particles can hop only in one direction with site dependent quenched random rates.…”

Phase diagram and edge effects in the ASEP with bottlenecks

“…It is well known that in nonequilibrium systems even weak disorder can lead to drastic changes [16,17]. For driven diffusive systems already a single defect site, i.e.…”

Active transport and cluster formation on 2D networks

“…fig. 3(b)), the exponential background of free particles must be added, hence P (m) ∼ P m0 (m)+1/m r exp(−m/m r ) where m r is the scale of random clusters 11 . This behavior corresponds to fig.…”

“…11 where a bulge over an exponential is exhibited. However, if ρ * (a) is 11 Note that due to the attractive interaction of filaments a lateral aggregation of particles is induce that locally increases the density compared to the average density ρ 0 p . This leads to an increased size scale of random clusters exceeded the critical density is exceeded cluster cascades can develop.…”

“…Jams can form in one dimensional systems with single tracks due to boundary conditions (boundary induced phase transitions [9]), induced by defects [10,11,12,13,14,15] or they emerge spontaneously due to stochastic slow down of vehicles in highway traffic [16,17].…”