Synchronized shocks in an inhomogeneous exclusion process

We study an exclusion process with 4 segments, which was recently introduced by T Banerjee, N Sarkar and A Basu [J. Stat. Mech. (2015) P01024]. The segments have hopping rates 1, r(<1), 1 and r, respectively. In a certain parameter region, two shocks appear, which are not static but synchronized. We explore dynamical properties of each shock and correlation of shocks, by means of the so-called second-class particle. The mean-squared displacement of shocks has three diffusive regimes, and the asymptotic diffusion coefficient is different from the known formula. In some time interval, it also exhibits sub-diffusion, being proportional to t^{1/2} . Furthermore we introduce a correlation function and a crossover time, in order to quantitatively characterize the synchronization. We numerically estimate the dynamical exponent for the crossover time. We also revisit the 2-segment case and the open boundary condition for comparison.Comment: 9 pages, 6 figures. v2: +3 reference

Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries

The misanthrope process is a class of stochastic interacting particle systems, generalizing the simple exclusion process. It allows each site of the lattice to accommodate more than one particle. We consider a special case of the one dimensional misanthrope process whose probability distribution is completely equivalent to the ordinary simple exclusion process under the periodic boundary condition. By imposing open boundaries, high- and low-density domains can coexist in the system, which we investigate by Monte Carlo simulations. We examine finite-size corrections of density profiles and correlation functions, when the jump rule for particles is symmetric. Moreover, we study properties of delocalized and localized shocks in the case of the totally asymmetric jump rule. The localized shock slowly moves to its stable position in the bulk.Comment: 8 pages, 7 figures. v2: minor changes. v3: changed the structure of the work, added 7 references, replaced some figure

Density profiles of the exclusive queueing process

The exclusive queueing process (EQP) incorporates the exclusion principle into classic queueing models. It can be interpreted as an exclusion process of variable system length. Here we extend previous studies of its phase diagram by identifying subphases which can be distinguished by the number of plateaus in the density profiles. Furthermore the influence of different update procedures (parallel, backward-ordered, continuous time) is determined

Critical behavior of the exclusive queueing process

The exclusive queueing process (EQP) is a generalization of the classical M/M/1 queue. It is equivalent to a totally asymmetric exclusion process (TASEP) of varying length. Here we consider two discrete-time versions of the EQP with parallel and backward-sequential update rules. The phase diagram (with respect to the arrival probability \alpha\ and the service probability \beta) is divided into two phases corresponding to divergence and convergence of the system length. We investigate the behavior on the critical line separating these phases. For both update rules, we find diffusive behavior for small output probability (\beta\beta_c it becomes sub-diffusive and nonuniversal: the exponents characterizing the divergence of the system length and the number of customers are found to depend on the update rule. For the backward-update case, they also depend on the hopping parameter p, and remain finite when p is large, indicating a first order transition.Comment: v2: published versio

Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry

We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement entropies from the double scaling limit. We also evaluate the geometric entanglement, which serves as another measure for entanglement. We find the geometric entanglement reaches its maximum at the isotropic point, and decreases with the increase of the anisotropy. This behavior is similar to that of the entanglement entropies

Effective ergodicity breaking in an exclusion process with varying system length

Stochastic processes of interacting particles with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.Comment: 5 pages, 7 figure

Two dimensional outflows for cellular automata with shuffle updates

In this paper, we explore the two-dimensional behavior of cellular automata with shuffle updates. As a test case, we consider the evacuation of a square room by pedestrians modeled by a cellular automaton model with a static floor field. Shuffle updates are characterized by a variable associated to each particle and called phase, that can be interpreted as the phase in the step cycle in the frame of pedestrian flows. Here we also introduce a dynamics for these phases, in order to modify the properties of the model. We investigate in particular the crossover between low- and high-density regimes that occurs when the density of pedestrians increases, the dependency of the outflow in the strength of the floor field, and the shape of the queue in front of the exit. Eventually we discuss the relevance of these results for pedestrians.Comment: 20 pages, 5 figures. v2: 16 pages, 5 figures; changed the title, abstract and structure of the paper. v3: minor change

Reply to "Comment on Generalized Exclusion Processes: Transport Coefficients"

We reply to the comment of Becker, Nelissen, Cleuren, Partoens, and Van den Broeck, Phys. Rev. E 93, 046101 (2016) on our article, Phys. Rev. E 90, 052108 (2014) about transport properties of a class of generalized exclusion processes.Comment: 2 pages, 1 figur