Joule-Thomson coefficient of ideal anyons within fractional exclusion statistics

Abstract

The analytical expressions of the Joule-Thomson coefficient for homogeneous and harmonically trapped three-dimensional ideal anyons which obey Haldane fractional exclusion statistics are derived. For an ideal Fermi gas, the Joule-Thomson coefficient is negative, which means that there is no maximum Joule-Thomson inversion temperature. With careful study, it is found that there exists a Joule-Thomson inversion temperature in the fractional exclusion statistics model. Furthermore, the relations between the Joule-Thomson inversion temperature and the statistical parameter g are investigated.

Adiabatic sound velocity and compressibility of a trapped d-dimensional ideal anyon gas

“…As discussed in the third paragraph of the introduction part, there is µ 0 = ξ 1/2 ǫ F for a zero-temperature trapped unitary Fermi gas. Comparing µ 0 = g 1/3 ǫ F with µ 0 = ξ 1/2 ǫ F , one can find that the relation between the statistical parameter g and the universal constant ξ is g = ξ 3/2 [6,7,8]. Consequently, the final result is…”

“…Due to the scale invariance, the thermodynamic quantities of the unitary Fermi gas and the Haldane anyon gas are both related with the corresponding quantities of the ideal Fermi gas at zero temperature. Therefore, it is assumed that the threedimensional anyon gas obeying fractional exclusion statistics can be used to model the statistical behavior of a Fermi system at unitarity [6,7,8,9]. In addition, the finite-temperature internal energy and entropy of the ideal anyons within Haldane statistics are in good agreement with experimental data of the unitary fermions for a given statistical parameter g [7].…”

“…Following the distribution function of the Haldane anyon gas given by Wu [2], the thermodynamics of ideal anyons was a focus of theoretical attention 1 Email: qinfang.phy@gmail.com 2 Email: chenjs@iopp.ccnu.edu.cn in the past few years [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. For example, the thermodynamics of the ideal anyons in two dimensions has been investigated [3,4,5], and the analytical expressions for the chemical potential, internal energy, entropy, isochore and isobar heat capacities, and Joule-Thomson coefficient of a three-dimensional ideal anyon gas have been derived in the previous works [6,7,8,9]. Furthermore, the thermodynamics for a homogeneous ideal gas within fractional exclusion statistics has been studied in some detail in arbitrary dimensions by Refs.…”

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]). …”

“…A stochastic method for the simulation of the time evolution of FES systems was introduced in Ref. [26] as a generalization of a similar method used for Bose and Fermi systems [27], whereas the relatively recent experimental realization of the Fermi degeneracy in cold atomic gases has renewed the interest in the theoretical investigation of non-ideal Fermi systems at low temperatures and their interpretation as ideal FES systems [23,[28][29][30][31].…”