Facilitated asymmetric exclusion

Quest for the golden ratio universality class

Using mode-coupling theory, the conditions for all allowed dynamical universality classes for the conserved modes in one-dimensional driven systems are presented in closed form as a function of the stationary currents and their derivatives. With an eye on the search for the golden ratio universality class, the existence of some families of microscopic models is ruled out a priori by using an Onsager-type macroscopic current symmetry. In particular, if the currents are symmetric or antisymmetric under the interchange of the conserved densities, then at equal mean densities the golden modes can only appear in the antisymmetric case and if the conserved quantities are correlated, but not in the symmetric case where at equal densities one mode is always diffusive and the second may be either Kardar-Parisi-Zhang (KPZ), modified KPZ, 3/2-Lévy, or also diffusive. We also show that the predictions of mode-coupling theory for a noisy chain of harmonic oscillators are exact.

Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores

The system of driven dense colloid mixtures is studied in one-, two-, and three-dimensional geometries. We calculate the diffusion coefficients and mobilities for each particle type, including cross-terms, in a hydrodynamic limit, using a mean-field-type approximation. The set of nonlinear diffusion equations are then solved. In one dimension, analytical results are possible. We show that in mixtures, the "Brazil nut" phenomenon, or depletion of larger particles by force of smaller ones, appears quite generically. We calculate the ratchet current and quantify the capability of sorting particles according to their size. We also indicate that the "Brazil nut" effect lies behind the possibility of perfect separation, where large and big particles travel in strictly opposite direction.

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores

The system of a driven dense colloid mixture in a tube with diameter comparable to particle size is modeled by a generalization of the asymmetric simple exclusion process (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site and by considering two species of particles, which differ in size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of the Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results. However, for long-range correlations, we show that the Kirkwood approximation is useless, as it predicts exponential decay of the density-density correlation function with distance, while simulation data indicate that the decay is algebraic. For the one-component system, we show that the decay is governed by a power law with universal exponent close to 2. In the two-component system, the correlation function behaves in a more complicated manner: Its sign oscillates but the envelope decays again very slowly and the decay is compatible with a power law with an exponent somewhat lower than 2. Therefore, our generalization of the ASEP belongs to a different universality class from the ensemble of generalized ASEP models which are mappable to zero-range processes.

Slow dynamics and large deviations in classical stochastic Fredkin chains

The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground-state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPSs). The stochastic model displays slow dynamics, including power-law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations-which we compute accurately via numerical MPSs-including an active-inactive phase transition and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.

Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics

Multilane totally asymmetric simple exclusion processes with interactions between the lanes have recently been investigated actively. This paper proposes a two-lane model with extended Langmuir kinetics on a periodic lattice. Both bidirectional and unidirectional flows are investigated. In our model, the hopping, attachment, and detachment rates vary depending on the state of the corresponding site in the other lane. We obtain a theoretical expression for the global density of the system in the steady state from three kinds of mean-field analyses [(1×1)-, (2×1)-, and (2×2)-cluster cases]. We verify that the (2×2)-cluster mean-field analysis reproduces the differences between the two directional flows and approximates well the results of computer simulations for some cases. We observe that (2×1)-cluster mean-field analyses are already good approximations of the simulation results for unidirectional flows; on the other hand, the accuracy of the approximations much improves by (2×2)-cluster one for bidirectional flows. We explain the phenomena in a qualitative manner by a simple analysis of correlations. We expect these findings to give informative suggestions for actual traffic systems.

Exponential decay of spatial correlation in driven diffusive system: A universal feature of macroscopic homogeneous state

Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems.

Totally asymmetric exclusion process fed by using a non-Poissonian clock

In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function.

Exclusion processes with avalanches

In an exclusion process with avalanches, when a particle hops to a neighboring empty site which is adjacent to an island the particle on the other end of the island immediately hops, and if it joins another island this triggers another hop. There are no restrictions on the length of the islands and the duration of the avalanche. This process is well defined in the low-density region ρ < 1/2. We describe the nature of steady states (on a ring) and determine all correlation functions. For the asymmetric version of the process, we compute the steady state current, and we describe shock and rarefaction waves which arise in the evolution of the step-function initial profile. For the symmetric version, we determine the diffusion coefficient and examine the evolution of a tagged particle.

Accelerated transport and growth with symmetrized dynamics

In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in 1+1 dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the "distance of interaction" denoted by ℓ(max). We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening of the cluster size distribution for cluster sizes above ℓ(max), when compared with the ordinary totally asymmetric exclusion process (TASEP). We also characterize the difference between the TASEP, AEP, and DAEP by computing a "staggered" order parameter, which reveals the local order in the steady state. This order in part explains the behavior of the particle current as a function of density. The differences of the steady states are also reflected by the behavior of the temporal and spatial correlation functions in the interface picture.

Contact processes in crowded environments

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions (contacts) between particles in the steady state limit, while in the active phase collisions persist. To investigate this system at higher densities, we construct and study a conserved-particle-number contact process with three-body interactions, which are potentially more likely than two-body interactions at higher densities. For example, consider one active (diffusing) particle colliding with two inactive (nondiffusing) particles such that they become active and consider spontaneous inactivation. In mean field, this system exhibits a continuous dynamical phase transition. Simulations on square lattices also indicate a continuous transition with exponents similar to those measured for the conserved lattice gas (CLG) model. In contrast, the three-body interaction requiring two active particles to activate one inactive particle exhibits a discontinuous transition. Finally, inspired by kinetically constrained models of the glass transition, we investigate the "caging effect" at even higher particle densities to look for a second dynamical phase transition back to an inactive phase. Square lattice simulations suggest a continuous transition with a new set of exponents differing from both the CLG model and what is known as directed percolation, indicating a potentially new universality class for a contact process with a conserved particle number.

Limiting shapes in two-dimensional Ising ferromagnets

We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by √[t], the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.

Mass transport perspective on an accelerated exclusion process: analysis of augmented current and unit-velocity phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ≤ℓ(max). With various choices of the interaction range, ℓ(max), we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

Entrainment and unit velocity: surprises in an accelerated exclusion process

We introduce a class of distance-dependent interactions in an accelerated exclusion process inspired by the observation of transcribing RNA polymerase speeding up when "pushed" by a trailing one. On a ring, the accelerated exclusion process steady state displays a discontinuous transition, from being homogeneous (with augmented currents) to phase segregated. In the latter state, the holes appear loosely bound and move together, much like a train. Surprisingly, the current-density relation is simply J=1-ρ, signifying that the "hole train" travels with unit velocity.

Driving kinetically constrained models into nonequilibrium steady states: Structural and slow transport properties

Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at a theoretical level and by molecular dynamic simulations. To understand some of these features we study a schematic model of a highly viscous liquid, the two-dimensional Kob-Andersen kinetically constrained model, driven into nonequilibrium steady states by a uniform non-Hamiltonian force. We present a detailed numerical analysis of the microscopic behavior of the model, including transversal and longitudinal spatial correlations and dynamic heterogeneities. In particular, we show that at high particle density the transition from positive to negative resistance regimes in the current vs field relation can be explained via the emergence of nontrivial structures that intermittently trap the particles and slow down the dynamics. We relate such spatial structures to the current vs field relation in the different transport regimes.

Phase transitions induced by competition of two driven parts in a periodic system

This paper studies a periodic driven diffusive system, which separates into two equal-sized parts with different values of hopping rates. Competition of the two different driven parts leads to various bulk-driven phase transitions, including shock and antishock. More interestingly, for the symmetric scenario, one can observe shock and antishock simultaneously in the system. We have explained the coexistence of shock and antishock via the effective boundary reservoir density. Theoretical analysis has been carried out to characterize the emerging nonequilibrium steady states, which is in good agreement with Monte Carlo simulations.