Two-parametric fractional statistics models for anyons
Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., 79005 Lviv, Ukraine
Received: 13 March 2014
Received in final form: 6 May 2014
Published online: 1 August 2014
In the paper, two-parametric models of fractional statistics are proposed in order to determine the functional form of the distribution function of free anyons. From the expressions of the second and third virial coefficients, an approximate correspondence is shown to hold for three models, namely, the nonadditive Polychronakos statistics and both the incomplete and the nonadditive modifications of the Haldane-Wu statistics. The difference occurs only in the fourth virial coefficient leading to a small correction in the equation of state. For the two generalizations of the Haldane-Wu statistics, the solutions for the statistics parameters g,q exist in the whole domain of the anyonic parameter α ∈ [0; 1], unlike the nonadditive Polychronakos statistics. It is suggested that the search for the expression of the anyonic distribution function should be made within some modifications of the Haldane-Wu statistics.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2014