2007/12/29 by J. W. van de Leur, J.W. van de Leur, van de Leur, J. W. +2
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories #cond-mat.dis-nn #cond-mat.other #math-ph #math.MP #math.PR #nlin.SI
paper · pdf · doi:10.48550/arxiv.0801.0066
23 pages, 2 figures, has been reported on the workshop "Random and integrable models in mathematics and physics" in Brussel, September 11-15, 2007
arxiv created 2007/12/29 · openalex publication_date 2007/12/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a version of random motion of hard core particles on the semi-lattice 1, 2, 3,..., where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a particle is created at the origin (namely, at site 1) provided that site 1 is free and (c) a particle is eliminated at the origin (provided that the site 1 is occupied). Relations to the BKP equation are explained. Namely, the tau functions of two different BKP hierarchies provide generating functions respectively (I) for transition weights between different particle configurations and (II) for an important object: a normalization function which plays the role of the statistical sum for our non-equilibrium system. As an example we study a model where the hopping rate depends on two parameters (r and β). For time \time→∞ we obtain the asymptotic configuration of particles obtained from the initial empty state (the state without particles) and find an analog of the first order transition at β=1.