Spontaneous breaking of translational invariance in one-dimensional stationary states on a ring

Arndt, Peter F.; Heinzel, T.; Rittenberg, V.

doi:10.1088/0305-4470/31/2/001

Cited by 108 publications

(179 citation statements)

References 22 publications

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“…The model thus defined is translationally invariant and the numbers of positive and negative particles are conserved. The study presented in [6] suggests the existence of three phases in the stationary state. In particular, as we shall see, for two of these phases charge segregation (segregation of species) occurs in the system.…”

Section: Introductionmentioning

confidence: 92%

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Arndt

Heinzel²,

Rittenberg

1999

Journal of Statistical Physics

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We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. The model depends on two parameters.Analytic calculations using quadratic algebras, inhomogeneous solutions of the mean-field equations and Monte-Carlo simulations suggest that the model has three phases. A pure phase in which one has three pinned blocks of only positive, negative particles and vacancies and in which translational invariance is broken. A mixed phase in which the current has a linear dependence on one parameter but is independent of the other one and of the density of the charged particles. In this phase one has a bump and a fluid. The bump (condensate) contains positive and negative particles only, the fluid contains charged particles and vacancies uniformly distributed. The mixed phase is separated from the disordered phase by a second-order phase-transition which has many properties of the Bose-Einstein phase-transition observed in equilibrium. Various critical exponents are found.

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Section: Introductionmentioning

confidence: 92%

“…In this model, introduced in [6], positive and negative particles diffuse in an asymmetric, CP invariant way. The positive particles hop clockwise, the negative particles counter-clockwise and oppositely charged adjacent particles may exchange positions.…”

Section: Introductionmentioning

confidence: 99%

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Arndt

Heinzel²,

Rittenberg

1999

Journal of Statistical Physics

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“…Arndt et al [288] considered a system of positive and negative charged particles diffusing on a ring in opposite directions. Positive particles move to an empty right neighbour and negative particles move to an empty left neighbour with the same rate λ.…”

Section: Generalizations Of the Tasepmentioning

confidence: 99%

Statistical physics of vehicular traffic and some related systems

2000

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In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

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“…In this case the system is predicted to phase separate at any density. Models for which J n decays exponentially to zero with n have been analyzed in the past and indeed were shown to exhibit phase separation [3][4][5].The results presented above emerge from a careful analysis of a zero-range process (ZRP) which could be viewed as a generic model for domain dynamics in one dimension. To define this process we consider a onedimensional lattice of M sites, or "boxes," with periodic boundary conditions.…”

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Criterion for Phase Separation in One-Dimensional Driven Systems

et al. 2002

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A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steadystate currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided. DOI: 10.1103/PhysRevLett.89.035702 PACS numbers: 64.75. +g, 05.20. -y The existence of phase separation and spontaneous symmetry breaking in low-dimensional systems far from thermal equilibrium has been a subject of recent interest [1,2]. While it is well known that these phenomena do not take place in one dimension in thermal equilibrium, several models of driven one-dimensional systems with local dynamics have recently been demonstrated to exhibit both [3 -5]. Whether or not a given model exhibits phase separation is in many cases not a simple question to answer, and it may depend on numerical evidence which could be rather subtle.For example, in a recent three-species model introduced by Arndt et al. [4] (AHR), it has been suggested that one should expect two distinct phase separated states: one in which the three species are fully separated from each other (related to the phase separation observed by Evans et al.[3] in a related model) and the other is a more subtle mixed state whose existence is supported by extensive numerical simulations of systems of finite length and by a meanfield treatment. Subsequently, an analytical analysis of the model has shown that the mixed state is in fact disordered and that in order to see this in simulations one has to study extremely long systems (of the order of 10 70 ), far beyond existing numerical capabilities [6].In another example introduced by Korniss et al. a twolane extension of a three-species driven system was studied [7]. It has been suggested that while for this model the one-lane system does not exhibit phase separation [8], this phenomenon does exist in the two-lane model. The studies rely on numerical simulations of systems of length up to 10 4 . This result is rather surprising and not well understood. It may very well be the case that as for the AHR model, the two-lane model does not actually exhibit phase separation in the thermodynamic limit and that this could be seen only by studying extremely long systems. It would thus be of great importance to find other criteria, which could distinguish between models supporting phase separation from those which do not.In this Letter we introduce a simple general criterion for the existence of phase separation in density-conserving one-dimensional driven systems. Phase separation is usually accompanied by a coarsening process in which small domains of, say, the high density phase coalesce, eventually leading to macroscopic phase separation. This process takes place as domains exc...

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Spontaneous breaking of translational invariance in one-dimensional stationary states on a ring

Cited by 108 publications

References 22 publications

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Statistical physics of vehicular traffic and some related systems

Criterion for Phase Separation in One-Dimensional Driven Systems

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