The interpolation approach to nonextensive quantum systems

TL;DR

This paper applies the interpolation approximation to nonextensive quantum systems, analyzing its accuracy and effects on physical properties across various phenomena, and compares it with the factorization approximation which tends to overestimate nonextensivity.

Contribution

It introduces the application of the interpolation approximation to nonextensive quantum systems and compares its effectiveness with the factorization approximation.

Findings

The interpolation approximation agrees with exact results within certain limits.

The factorization approximation overestimates nonextensivity.

The interpolation approximation provides more appropriate results for fermion systems.

Abstract

Recently it has been shown by the present author [H. Hasegawa, Phys. Rev. E (in press): arXiv:0904.2399] that the interpolation approximation (IA) to the generalized Bose-Einstein and Femi-Dirac distributions yields results in agreement with the exact ones within the $O(q-1)$ and in high- and low-temperature limits, where $(q-1)$ expresses the non-extensivity: the case of $q=1$ corresponding to the conventional quantal distributions. In this study, we have applied the generalized distributions in the IA to typical nonextensive subjects: (1) the black-body radiation, (2) the Bose-Einstein condensation, (3) the BCS superconductivity and (4) itinerant-electron (metallic) ferromagnetism. Effects of the non-extensivity on physical quantities in these nonextenisive quantum systems have been investigated. A critical comparison is made between results calculated by the IA and the factorization approximation (FA) which has been so far applied to many nonextensive systems. It has been pointed out that the FA overestimates the non-extensivity and that it leads to an inappropriate results for fermion systems like the subjects (3) and (4).