Critical Temperature For Bose-Einstein Condensation Research Articles

Gibbs ensembles in relativistic classical and quantum mechanics

Classical and quantum Gibbs ensembles are constructed for equilibrium statistical mechanics in the framework of an extension to many-body theory of a relativistic mechanics proposed by Stueckelberg. In addition to the usual chemical potential in the grand canonical ensemble, there is a new potential corresponding to the mass degree of freedom of relativistic systems. It is shown that in the nonrelativistic limit the relativistic ensembles we have obtained reduce to the usual ones, and mass fluctuations for the free-particle gas approach the fluctuations in N. The ultrarelativistic limit of the canonical ensemble for the free-particle gas differs from the corresponding limit of the ensemble proposed by Jüttner and Pauli. Due to the mass degree of freedom, the quantum counting of states is different from that of the nonrelativistic theory. If the mass distribution is sufficiently sharp, the thermodynamical effects of this multiplicity will not be large. There may, however, be detectable effects such as a shift in the Fermi level and the critical temperature for Bose-Einstein condensation, and some change in specific heats.

On the influence of exciton-exciton interaction on the critical temperature of Bose-Einstein condensation

Under the assumption of a sufficiently large concentration of a weakly repulsive interacting exciton system the realization of the “superfluid” state of this system is theoretically possible. This paper deals with the influence of the interaction on the critical temperature of the Bose-Einstein condensation with application to the case of the lowest exciton states in a benzene crystal using previous results (Majernikova E.: Czech. J. Phys.B 18 (1968), 830). It has been found that this interaction causes a rapid decrease of the critical temperature.