2000/12/27 by Peter F. Arndt, Arndt, Peter F., Vladimir Rittenberg +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cellular Automata and Lattice Gases (nlin.CG) #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.AP #math.DS #math.MP #nlin.CG #nlin.PS
paper · pdf · doi:10.48550/arxiv.cond-mat/0012480
openalex publication_date 2000/12/27 · arxiv created 2001/01/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We further study the stochastic model discussed in Ref.[2] in which positive\nand negative particles diffuse in an asymmetric, CP invariant way on a ring.\nThe positive particles hop clockwise, the negative counter-clockwise and\noppositely-charged adjacent particles may swap positions. We extend the\nanalysis of this model to the case when the densities of the charged particles\nare not the same. The mean-field equations describing the model are coupled\nnonlinear differential equations that we call the two-component Burgers\nequations. We find roundabout weak solutions of these equations. These\nsolutions are used to describe the properties of the stationary states of the\nstochastic model. The values of the currents and of various two-point\ncorrelation functions obtained from Monte-Carlo simulations are compared with\nthe mean-field results. Like in the case of equal densities, one finds a pure\nphase, a mixed phase and a disordered phase.\n