Statistical Mechanics and Thermodynamic Properties of Bose-Einstein Condensation in Fractal Media

A quantum statistical mechanics model for the BEC phenomenon in fractal media is formulated. This model is based upon the generalized nonextensive Tsallis thermostatistics. The thermodynamic behavior this formulation (the temperature dependence of the condensate thermodynamic properties) is also investigated. In addition to the formulated nonextensive model, a model for bosons harmonically trapped in fractal media based on the extensive thermostatistics is also adopted and its thermodynamic behavior is investigated.The thermodynamic behaviors of the two models (the extensive and the nonextensive) are compared. The comparisons are carried out for two standard fractals (the Sierpinski carpet and the Menger sponge). One of them is topologically embedded in 2D and the other is embedded in 3D.The comparisons reveal that the condensation temperature within the Tsallis (nonextensive) thermostatistics is always less than the corresponding one in the Boltzmann–Gibbs (extensive)mostatistics.Consequently, the condensate thermodynamic properties in Tsallis thermostatistics are always shifted to lower temperatures. These comparisons also show that despite the thermodynamic behaviors for the two ermostatistics are, in general,similar; the condensate thermodynamic properties seem to possess different temperature responses (slopes). The disagreement in the condensation temperature between the two hermostatistics is also justified.