About an alternative distribution function for fractional exclusion statistics

We show that it is possible to replace the actual implicit distribution function of the fractional exclusion statistics by an explicit one whose form does not change with the parameter α. This alternative simpler distribution function given by a generalization of Pauli exclusion principle from the level of the maximal occupation number is not completely equivalent to the distributions obtained from the level of state number counting of the fractional exclusion particles. Our result shows that the two distributions are equivalent for weakly bosonized fermions (α >> 0) at not very high temperatures. PACS : 05.30.-d,05.30.Pr,05.20.-y The principle of the fractional exclusion statistics (FES) was for the first time proposed about 60 years ago by Gentile[1] who suggested an intermediate maximum occupation number changing from 1 (for fermions) to ∞ (for bosons). This idea was later recognized and developed in the study of anyons and quasi-particle excitations for some low dimensional systems relevant to fractional quantum Hall effect and to superconductivity[2].