The interpolation approach to nonextensive quantum statistics

Abstract

Recently it has been shown by the present author [H. Hasegawa, Phys. Rev. E 80 (2009) 011126] that the interpolation approximation (IA) to the generalized Bose–Einstein and Fermi–Dirac distributions yields good results in agreement with the exact ones within the O ( q − 1 ) and in high- and low-temperature limits, where ( q − 1 ) expresses the nonextensivity: the case of q = 1 corresponding to the conventional quantal distributions. This paper reports applications of the IA to four nonextensive quantum subjects: (i) the black-body radiation, (ii) the Bose–Einstein condensation, (iii) the BCS superconductivity and (iv) itinerant-electron (metallic) ferromagnetism. Effects of the nonextensivity on physical quantities in these nonextensive quantum systems have been investigated. Comparisons between the calculated results and available observed data are made for the subjects (ii) and (iii). It has been pointed out that the factorization approximation (FA) which has been so far applied to many nonextensive systems, overestimates the nonextensivity and that it leads to inappropriate results for fermion systems like the subjects (iii) and (iv).