Thermodynamics in the NC disc

Abstract

We study the thermodynamics of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. We explicitly obtain expressions for thermodynamic potentials of gases of particles obeying different statistics. In order to do that, we derive an asymptotic expansion for the density of the zeros of Laguerre polynomials. As a result we prove that the Bose-Einstein condensation in the noncommutative disc does not take place.