We analytically calculate some thermodynamic quantities of an ideal
g-on gas obeying generalized exclusion statistics. We show that the specific heat of a
g-on gas (
g=0) vanishes linearly in any dimension as
T→0 when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at
g to the hole-statistics at
1/g at low temperatures. We derive the complete solution for the cluster coefficients
bl(g) as a function of Haldane's statistical interaction
g in
D dimensions. We also find that the cluster coefficients
bl(g) and the virial coefficients
al(g) are exactly mirror symmetric (
l=odd) or antisymmetric (
l=even) about
g=1/2. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the
g-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.
Abstract The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern–Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.
We achieve a bosonization of one-dimensional ideal gas of particles obeying exclusion statistics $\ensuremath{\lambda}$ (so called $\ensuremath{\lambda}$ exclusons) at low temperatures, resulting in a new variant of
c=1 conformal field theory with compactified radius $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\sqrt{1/\ensuremath{\lambda}}$. These ideal excluson gases exactly reproduce the low-
T critical properties of Luttinger liquids, so they can be used to characterize the fixed points of the latter. Generalized ideal gases with mutual statistics and nonideal gases with Luttinger-type interactions have also similar low-
T behavior, controlled by an effective statistics varying in a fixed-point line.
We discuss recent results on the relation between the strongly interacting one-dimensional Bose gas and a gas of ideal particles obeying nonmutual generalized exclusion statistics (GES). The thermodynamic properties considered include the statistical profiles, the specific heat and local pair correlations. In the strong coupling limit γ → ∞, the Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation from Fermi statistics during boson fermionization for finite but large interaction strength γ is described by the relation α ≈ 1 - 2/γ, where α is a measure of the GES. This gives a quantitative description of the fermionization process. In this sense the recent experimental measurement of local pair correlations in a 1D Bose gas of87Rb atoms also provides a measure of the deviation of the GES parameter α away from the pure Fermi statistics value α=1. Other thermodynamic properties, such as the distribution profiles and the specific heat, are also sensitive to the statistics. They also thus provide a way of exploring fractional statistics in the strongly interacting 1D Bose gas.