The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

Abstract

We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behavior, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behavior of the isochore heat capacity for a trapped unitary Fermi gas is also analyzed.

Finite temperature analytical results for a harmonically confined gas obeying exclusion statistics ind-dimensions

“…The integral in Eq (27). has already been addressed in an earlier work,[21] and following the same analysis, we readily obtain the desired result W (d) (r, p; T ) = 2 d g s )e −(r 2 +p 2 ) n (α) (ǫ n + k) (28). Similar to Eq.…”

“…Similar to Eq. (25), there is once again a clean separation of the variables in Eq (28),. which in this case are the spatial and momentum variables.…”

Joule-Thomson coefficient of ideal anyons within fractional exclusion statistics

“…The parameter g in the statistical model can be fixed as g = ξ 3/2 = 8 27 [35,36], where the universal constant ξ = 4 9 is given by the developed quasi-linear approximation [44][45][46][47][48][49]. By taking g = It is evident from figure 3 that the reduced JouleThomson inversion temperature increases with the increasing of the statistical parameter g. Further, the reduced inversion temperature of a homogeneous gas is higher than the corresponding one of a trapped gas with the same value of g. The difference in the reduced inversion temperatures between a homogeneous gas and a trapped gas becomes larger as g increases.…”

“…If ideal anyons are considered as quasiparticles to describe interactions [32][33][34][35][36], the effective mass is a significant physical quantity in the fractional exclusion statistics model.…”

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

“…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].…”