Fast Condensation in a tunable Backgammon model

Details Fast Condensation in a tunable Backgammon model Fast Condensation in a tunable Backgammon model

2006-01-24

arxiv.org/abs/cond-mat/0601532v1

Physics

Condensed Matter

Statistical Mechanics

Five page RevTeX file, seven eps figures

Scientific paper

We present a Monte Carlo study of the Backgammon model, at zero temperature, in which a departure box is chosen at random with a probability proportional to $(2\omega - 1)k + (1 - \omega)N$, where $k$ is the number of particles in the departure box and $N$ is the total number of particles (equivalently, boxes) in the system. The parameter $\omega \in [0,1]$ tunes the dynamics from being slow ($\omega = 1$) to being fast ($\omega = 0$). This parametrization tacitly assumes a two-box representation for the system at any instant of time and $\omega$ is formally related to the 'memory' parameter of a correlated binary sequence. For $\omega < 1/2$, the system undergoes a fast condensation beyond a certain time that depends on $\omega$ and the system size $N$. This condensation provides an interesting contrast to that studied with Zeta Urn model in that the probability that a box contains $k$ particles evolves differently in the model discussed here.

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