Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-12-29
Physics
Condensed Matter
Disordered Systems and Neural Networks
23 pages, 2 figures, has been reported on the workshop "Random and integrable models in mathematics and physics" in Brussel, S
Scientific paper
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 $\beta$). For time $\time\to\infty$ 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 $\beta=1$.
de Leur Johan W. van
Orlov Alexander Yu.
No associations
LandOfFree
Random turn walk on a half line with creation of particles at the origin does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Random turn walk on a half line with creation of particles at the origin, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random turn walk on a half line with creation of particles at the origin will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-260005