Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles

Schütz, Gunter M.

doi:10.1088/0305-4470/36/36/201

Cited by 135 publications

(138 citation statements)

References 192 publications

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“…However, one may naively expect that the creation of hernias is less important for PA and for the polymers with neutral and charged blocks. Despite its limited applicability to gel electrophoresis, our calculations provide exact asymptotic results for several classes of asymmetric simple exclusion processes with two types of of oppositely moving particles, 29 where the number of exact results is very limited. …”

Section: Discussionmentioning

confidence: 99%

Polymer dynamics in repton model at large fields

Kolomeisky

Drzewiński

2004

The Journal of Chemical Physics

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Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is found that for polyelectrolytes the drift velocity decreases exponentially as a function of the external field with an exponent depending on polymer size and parity, while for polyampholytes the drift velocity is independent of polymer chain size. However, for polymers, consisting of charged and neutral blocks, the drift velocity approaches the constant limit which is determined by the size of the neutral block. The theoretical arguments are supported by extensive numerical calculations by means of densitymatrix renormalization group techniques.

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Section: Discussionmentioning

confidence: 99%

Polymer dynamics in repton model at large fields

Kolomeisky

Drzewiński

2004

The Journal of Chemical Physics

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“…Some of these topics, however, have recently been reviewed elsewhere [28,29]. We also direct the reader to established reviews, such as [19,[30][31][32][33][34][35], for any other background that we have been forced to leave out here.…”

Section: Purpose Of This Reviewmentioning

confidence: 99%

Nonequilibrium steady states of matrix-product form: a solver's guide

Blythe

Evans²

2007

J. Phys. A: Math. Theor.

627

1,014

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Abstract. We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven diffusive systems-which includes exclusion processes-focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form. In addition to a gentle introduction to this matrix product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.

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“…In this situation, a critical role for understanding different complex phenomena in Chemistry, Physics and Biology is played by a class of low-dimensional non-equilibrium multiparticle models known as asymmetric simple exclusion processes (ASEP) [1,2,3,4,5]. ASEP are stochastic models where particle interact via an exclusion potential and move along discrete lattices.…”

Section: Introductionmentioning

confidence: 99%

Parallel coupling of symmetric and asymmetric exclusion processes

Tsekouras

Kolomeisky

2008

J. Phys. A: Math. Theor.

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Abstract.A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions. Theoretical calculations and computer simulations predict that inter-channel couplings have a strong effect on stationary properties. It is also argued that our results might be relevant for understanding multi-particle dynamics of motor proteins.

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Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles

Cited by 135 publications

References 192 publications

Polymer dynamics in repton model at large fields

Polymer dynamics in repton model at large fields

Nonequilibrium steady states of matrix-product form: a solver's guide

Parallel coupling of symmetric and asymmetric exclusion processes

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