Intermediate Statistics

Abstract

The distinctions between intermediate statistics, parastatistics, and Okayama statistics are discussed and it is pointed out that the distribution function of the intermediate statistics does not follow from the para-Fermi statistics. The partition function, the pressure, and the specific heat of free particles which obey intermediate statistics are calculated in one, two, and three dimensions.

Gentile statistics with a large maximum occupation number

“…A special case of ν = 3 and s = 2, without the ground state contribution, has been discussed in Ref. [1,3]. Our result shows that, the thermodynamic behavior of Gentile statistics, especially the contribution of the ground state for the case ν > s, depends sensitively on the maximum occupation number n.…”

“…If we ignore the contribution from the ground state or, equivalently, take N 0 = 0, the above thermodynamic quantities will return to the results given by Ref. [1,3]. However, since in Gentile statistics N 0 can take any value, the influence of the ground state must be reckoned in.…”

“…Specifically, we will study the contribution of the ground state to the thermodynamic quantities, which is ignored in Ref. [1,3].…”

“…The thermodynamic behavior of an ideal gas obeying Gentile statistics has been discussed in some literature [1,3]. Nevertheless, in these works the contribution from the ground state was ignored.…”

From creation and annihilation operators to statistics

“…Canonical examples are the Bose-Einstein distribution for the commutation relation [a, a † ] = 1 and the Fermi-Dirac distribution for the anti-commutation relation {a, a † } = 1. Starting from the pioneer works of Gentile [1] and Green [2], many different distributions have been proposed as extensions that go beyond or interpolate the statistics of bosons and fermions; see, for example, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”