Functional-differential equations for $F_q$%-transforms of $q$-Gaussians

Details Functional-differential equations for $F_q$%-transforms of $q$-Gaussians Functional-differential equations for $F_q$%-transforms of $q$-Gaussians

2008-02-02

arxiv.org/abs/0802.0264v2

J. Phys. A: Math. Theor. 43, 095202 (2010)

Physics

Condensed Matter

Statistical Mechanics

14 pages A new section on a related solution of the porous medium equation in comparison with the previous version has been in

Scientific paper

10.1088/1751-8113/43/9/095202

In the paper the question - Is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor? - is studied for the whole range of $q\in (-\infty, 3)$. This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. We prove that the answer is affirmative if and only if q > 1, excluding two particular cases of q<1, namely, q = 1/2 and q = 2/3, which are also out of the theory valid for q \ge 1. We also discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

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