Meinardus theorem and the asymptotic form of the quantum p-brane state density

Abstract

Within the semiclassical approximation for the p-branes (discrete mass spectrum) the asymptotic form of the density of states is obtained. The universal feature of the density, which grows slower than for black holes but faster than the one for strings, is found by using rigorous results due to Meinardus. In particular the explicit forms of the prefactors of the p-branes total level degeneracy are calculated. A brief physical discussion about the thermodynamic properties of an extended object is also presented.