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Evolutionary Genomics Group Department of Computational Molecular Biology |
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Title: Spontaneous breaking of translational invariance and spatial condensation in stationary states on a ring. I. The neutral system Authors: Peter F Arndt, Thomas Heinzel, Vladimir Rittenberg Abstract: 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 par- ticles hop clockwise, the negative counterclockwise, 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: ( 1 ) a pure phase in which one has three pinned blocks of only positive or negative particles and vacancies and in which translational invariance is broken; ( 2 ) 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 ) containing positive and negative particles only, the fluid containing charged particles and vacancies uniformly distributed; and ( 3 ) 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. Reference: Journal of Statistical Physics 97 (1999) 1-65 Links: [Journal] [Fulltext (pdf)] |