Scale invariance and related properties of q-Gaussian systems

Details Scale invariance and related properties of q-Gaussian systems Scale invariance and related properties of q-Gaussian systems

2006-12-15

arxiv.org/abs/cond-mat/0612393v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.physleta.2007.02.003

We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared with that applying for Gaussian distributions, with emphasis on dimensional considerations. In particular, a Gaussian system may be part of a larger system that is not Gaussian, but, if the larger system is spherically invariant, then it is necessarily Gaussian again. We show that this result extends to q-Gaussian systems via elliptic invariance. The problem of estimating the appropriate value for $q$ is revisited. A kinetic application is also provided.

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