Generalized exclusion processes: Transport coefficients

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

doi:10.1103/physreve.90.052108

Cited by 27 publications

(51 citation statements)

References 55 publications

(98 reference statements)

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“…Without any such potential, one has an SSEP with fixed (independent of space and time) hopping rates for the particles, which is an old problem [27] and has been intensively studied in the last few decades [28][29][30][31][32][33][34][35][36][37][38]. In the presence of a time-periodic potential, the hopping rates become explicit functions of time, which has not been explored much until recently [10,11,39].…”

Section: Introductionmentioning

confidence: 99%

Symmetric exclusion processes on a ring with moving defects

Chatterjee

Pradhan

2016

Phys. Rev. E

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We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders -a generalization of the model proposed earlier [Phys. Rev. E 89, 022138 (2014)]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.

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Section: Introductionmentioning

confidence: 99%

Symmetric exclusion processes on a ring with moving defects

Chatterjee

Pradhan

2016

Phys. Rev. E

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“…It is claimed that these expressions become exact in the hydrodynamic limit. In this Comment, we point out that (i) the influence of correlations upon the diffusion does not vanish in the hydrodynamic limit, and (ii) the expressions for the self-and transport diffusion derived by Arita et In a recent paper [1], Arita et al derived analytical expressions for the transport-diffusion coefficient in a generalized exclusion process. Their derivation depends crucially on the assumption that correlations in the dynamics can be ignored up to first order in the concentration gradient, at least in the hydrodynamic regime.…”

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confidence: 99%

“…This is the result from Ref. [1] for the self-diffusion, parametrized as a function of µ instead of λ = e −β(c−µ) . A similar, but more involved, calculation can be performed to show the equivalence of the expressions for the transport diffusion.…”

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Comment on “Generalized exclusion processes: Transport coefficients”

et al. 2016

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In a recent paper Arita et al. [Phys. Rev. E 90, 052108 (2014)] consider the transport properties of a class of generalized exclusion processes. Analytical expressions for the transport-diffusion coefficient are derived by ignoring correlations. It is claimed that these expressions become exact in the hydrodynamic limit. In this Comment, we point out that (i) the influence of correlations upon the diffusion does not vanish in the hydrodynamic limit, and (ii) the expressions for the self-and transport diffusion derived by Arita et al. are special cases of results derived in [Phys. Rev. Lett. 111, 110601 (2013)].

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Integrable Floquet dynamics, generalized exclusion processes and “fused” matrix ansatz

Vanicat

2018

Nuclear Physics B

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We present a general method for constructing integrable stochastic processes, with twostep discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current. 1 matthieu.vanicat@fmf.uni-lj.si 1 Introduction.Systems of particles in interaction on a one-dimensional lattice have attracted lots of attention in the last decades. The reason is twofold: on one hand they seem to capture the essential physical features of out-of-equilibrium systems, and on the other hand they allow in some particular cases for exact computations of physical quantities. In particular the study of exclusion processes, for which particles experience a hard-core interaction (there is at most one particle on each site of the lattice), turned out to be very fruitful. The Asymmetric Simple Exclusion Process (ASEP) is a paradigmatic example of such model [11,14]. The phase diagram of the continuous time model with open boundaries was exactly computed using a matrix product construction of the stationary state [15,41]. The ASEP was also studied in the discrete time setting using various stochastic update rules [39] (see also for instance [1] and references therein for more recent developments and applications to traffic flow). The matrix product ansatz was successfully used to solve the ASEP with discrete time parallel update and sequential update [25,26,40,39,18,22,49].The reason behind the exact solutions of these models is their integrability: the Markov matrix M ruling their stochastic dynamics is part of a family of commuting operators generated by a transfer matrix. The transfer matrix is constructed from a R-matrix satisfying the Yang-Baxter equation [5]. It is well known that continuous time Markov matrices with local stochastic rules can be obtained by taking the first logarithmic derivative of an appropriate transfer matrix. This mechanism is quite general and relies only on minor assumptions on the R-matrix (essentially the regularity property). It has also been observed that the transfer matrix of the six vertex ...

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Generalized exclusion processes: Transport coefficients

Cited by 27 publications

References 55 publications

Symmetric exclusion processes on a ring with moving defects

Symmetric exclusion processes on a ring with moving defects

Comment on “Generalized exclusion processes: Transport coefficients”

Integrable Floquet dynamics, generalized exclusion processes and “fused” matrix ansatz

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