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2016•Ukrainian Journal of PhysicsOpen access

Two-Parameter Modifications of Anyonic Statistics

M. Hornetska, Andrij Rovenchak

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Abstract

Two-parameter models of fractional statistics aimed at finding an expression for the occupation numbers of free anyons have been considered. Virial coefficients are found for statistics of several types: к-deformed Polychronakos and Haldane–Wu statistics, Polychronakos and Haldane–Wu statistics modified with the q-exponential in the bosonic limit, and incomplete and nonadditive Gentile statistics for various level-filling maxima. A relation between the anyonic statistics and various statistics of fractional types is found and analyzed.

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Two-parameter models of fractional statistics aimed at finding an expression for the occupation numbers of free anyons have been considered. Virial coefficients are found for statistics of several types: к-deformed Polychronakos and Haldane–Wu statistics, Polychronakos and Haldane–Wu statistics modified with the q-exponential in the bosonic limit, and incomplete and nonadditive Gentile statistics for various level-filling maxima. A relation between the anyonic statistics and various statistics of fractional types is found and analyzed.

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Available abstract

Two-parameter models of fractional statistics aimed at finding an expression for the occupation numbers of free anyons have been considered. Virial coefficients are found for statistics of several types: к-deformed Polychronakos and Haldane–Wu statistics, Polychronakos and Haldane–Wu statistics modified with the q-exponential in the bosonic limit, and incomplete and nonadditive Gentile statistics for various level-filling maxima. A relation between the anyonic statistics and various statistics of fractional types is found and analyzed.

Key concepts: Statistics, Topological quantum computer, Maxima, Summary statistics, Virial coefficient, Physics, Statistical physics, Mathematics

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