Thermodynamics of ideal quantum gas with fractional statistics in D dimensions

In a recent letter -Phys. Rev. Lett. 73, 3331 (1995)-, the conclusion was reached that, in the one-dimensional Calogero model, only the second virial coefficient is affected by the statistical parameter $\alpha$, where $\alpha$ is related to the coupling constant $\kappa/ x_{ij}^2$ of the Calogero interaction by $\kappa=\alpha(\alpha+1)$. We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particl...

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low temperature quantities have the same temperature dependences as for ...

We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and lo...

Using a proposed generalization of the pair distribution function for a gas of non-interacting particles obeying fractional exclusion statistics in arbitrary dimensionality, we derive the statistical correlations in the asymptotic limit of vanishing or low temperature. While Friedel-like oscillations are present in nearly all non-bosonic cases at T=0, they are characterized by exponential damping at low temperature. We discuss the dependence of these features on dimensionalit...

We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations, and in this connection point out a fundamental contrast to conventional quantum statistics. We demonstrate a duality relating the distribution of particles at statistics $g$ to the distribution of holes at statistics $1/g$. We suggest applications to Mott insulators.

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this paper I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles...

We develop a bosonization approach to study the low temperature properties of one-dimensional gas of particles obeying fractional exclusion statistics (FES). It is shown that such ideal gas reproduces the low-energy excitations and asymptotic exponents of a one-component Luttinger liquid (with no internal degrees of freedom). The bosonized effective theory at low energy (or temperature) is identified to a $c=1$ conformal field theory (CFT) with compactified radius determined ...

We report exact numerical calculation of chemical potential, condensate fraction and specific heat of $N$ non-interacting bosons confined in an isotropic harmonic oscillator trap in one, two and three dimensions, as also for interacting bosons in a 3D trap. Quasi phase transitions are observed in all these cases, including one-dimension, as shown by a rapid change of all the thermodynamic quantities at the transition point. The change becomes more rapid as $N$ increases in 2D...

The paper is concerned with thermostatistics of both $D$-dimensional Bose and Fermi ideal gases in a confining potential of type $Ar^{n}+Br^{-n}$. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like density of states, density profiles and number of particles. Bose-Einstein condensation (BEC) is discussed in the high and low temperature regimes.