Non-extensive quantum statistics with particle-hole symmetry

Biró, Tamás Sándor and Shen, K. M. and Zhang, B. W. (2015) Non-extensive quantum statistics with particle-hole symmetry. PHYSICA A - STATISTICAL MECHANICS AND ITS APPLICATIONS, 428. pp. 410-415. ISSN 0378-4371

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Abstract

Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further requirements arise from the symmetric handling of particles and holes (excitations above and below the Fermi level). Naive replacements of the exponential function or ”cut and paste” solutions fail to satisfy this symmetry and to be smooth at the Fermi level at the same time. We solve this problem by a general ansatz dividing the deformed exponential to odd and even terms and demonstrate that how earlier suggestions, like the κ- and q-exponential behave in this respect.

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