Polychronakos fractional statistics with a complex-valued parameter

Abstract

A generalization of quantum statistics is proposed in a fashion similar to the suggestion of Polychronakos [Phys. Lett. B 365, 202 (1996)] with the parameter α varying between -1 (fermionic case) and +1 (bosonic case). However, unlike the original formulation, it is suggested that intermediate values are located on the unit circle in the complex plane. In doing so one can avoid the case α = 0 corresponding to the Boltzmann statistics, which is not a quantum one. The limits of α → +1 and α → -1 reproducing small deviations from the Bose and Fermi statistics, respectively, are studied in detail. The equivalence between the statistics parameter and a possible dissipative part of the excitation spectrum is established. The case of a non-conserving number of excitations is analyzed. It is defined from the condition that the real part of the chemical potential equals zero. Thermodynamic quantities of a model system of two-dimensional harmonic oscillators are calculated. © Published under licence by IOP Publishing Ltd.