Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics

Abstract

After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional exclusion statistics. The effect of dimensionality is one focal point, the ratio µ/kBT of chemical potential to thermal energy being obtained numerically as a function of a scaled particle density. Pair correlation functions are also presented as a function of the statistical parameter, with 'Friedel' oscillations developing close to the fermion limit, for sufficiently large density.

Statistical correlations of an anyon liquid at low temperatures

“…Therefore, the absence of Friedel-like oscillations in the pair correlation function (cf. Figure 1(b), for T ¼ 0, and Reference [9] for finite temperature) can only be related to the presence of the vanishing factor cos() in the original definition of the pair correlation function, Equation (1). Indeed, in this case the factor cos() cancels every deviation of g(r) from unity.…”

“….i denotes a quantum statistical average associated with the equilibrium distribution of the identical particle assembly under analysis. In Reference [9], we introduce a particular generalisation of the commutation relations for the -fields, interpolating between boson and fermion statistics for 0 1 and arbitrary dimensionality d. These are reminiscent of the graded commutation relations of Greenberg [11], weakly violating conventional quantum statistics.…”

“…Recently, the statistical correlations of an ideal gas of particles obeying fractional exchange statistics have been addressed, in arbitrary dimensionality, as a function of density, temperature and statistical parameter , partly analytically and partly numerically, through the study of the pair correlation function g(r) [9]. This function represents the probability of simultaneously finding two anyons at positions r and r ¼ 0, respectively.…”

Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting-particle systems in any number of dimensions

“…This has been a prolific concept and was applied to both quantum and classical systems (see e.g. [3,4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]). …”

Fractional exclusion statistics applied to relativistic nuclear matter

“…[1], received very much attention since its discovery and has been applied to many models of interacting particle systems and ideal gases in different external conditions (see for example Refs. [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]). Nevertheless, some of the basic properties of the model eventually have been deduced only recently [20,17] and a general ansatz regarding the parameters of the FES have been introduced and applied in Refs.…”