Bose-Einstein condensation and a two-dimensional walk model

Details Bose-Einstein condensation and a two-dimensional walk model Bose-Einstein condensation and a two-dimensional walk model

2011-01-09

arxiv.org/abs/1101.1669v2

Physics

Condensed Matter

Statistical Mechanics

5 pages, 1 figure, Accepted for publication in PRE (2011)

Scientific paper

We introduce a two-dimensional walk model in which a random walker can only move on the first quarter of a two-dimensional plane. We calculate the partition function of this walk model using a transfer matrix method and show that the model undergoes a phase-transition. Surprisingly the partition function of this two-dimensional walk model is exactly equal to that of a driven-diffusive system defined on a discrete lattice with periodic boundary conditions in which a phase transition occurs from a high-density to a low-density phase. The driven-diffusive system can be mapped to a zero-range process where the particles can accumulate in a single lattice site in the low-density phase. This is very reminiscent of real-space Bose-Einstein condensation.

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