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Title Self-similarity degree of deformed statistical ensembles
Authors Oliemskoi, Oleksandr Ivanovych
Shuda, Iryna Oleksandrivna
Vaylenko, A.S.
Keywords self-similarity
dilatation
jackson derivative
homogeneous function
Type Article
Date of Issue 2009
URI http://essuir.sumdu.edu.ua/handle/123456789/3032
Publisher Physica A
License
Citation Olemskoy, A.I. Self-similarity degree of deformed statistical ensembles [Текст] / A.I. Olemskoy, I.O. Shuda, A.S. Vaylenko // Physica A. — 2009. — vol.388. — pp. 1929-1938
Abstract We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. The related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree q fixed by the condition of invariance under (n+1)- fold action of the related dilatation operator. In slightly deformed phase space, we find the homogeneous function is defined with the linear dependence at n=0, whereas the self-similarity degree equals the gold mean at n=1, and q->1 in the limit n->(infinite). Dilatation of the homogeneous function is shown to decrease the self-similarity degree q at n>0. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3032
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