Thermodynamics of ideal quantum gas with fractional statistics in D dimensions

It is mentioned that anyon thermodynamic potential $Q(\alpha, N)$ could not be factorized in terms characteristic of the ideal boson $\alpha =0$ and fermion $\alpha =1$ gases by the relation $Q(\alpha, N) = (1-\alpha) Q(0, N_b)+ \alpha Q(1, N_f)$ in which $N=N_f +N_b$, that claimed in Phys. Rev. Lett. 78, 3233 (1997). Our analyses indicate that the thermodynamic quantities of anyon gas may be factorized as $Q(\alpha) = \alpha Q(1) + (1-\alpha) Q(0)$ only in the two-dimension ...

We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of identical or different momenta. Thus, the thermodynamic properties of these systems can be characterized by the generalized ideal gases recently proposed by one of us. For example, the Yang-Yang $\delta$-function gas is a gas with specific statis...

This paper is concerned with statistical properties of a gas of $qp$-bosons without interaction. Some thermodynamical functions for such a system in $D$ dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters $q$ and $p$. Finally, the second-order correlation function of a gas of photons is calculated.

The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an illustration, one considers the anyon model restricted to the lowest Landau level of a strong magnetic field at low temperature, the generalization of this model to several particles species, and the one dimensional Calogero model. One revie...

From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in $d=3$ and $d=2$. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap t...

Haldane fractional exclusion statistics (FES) has a long history of intense studies, but its realization in physical systems is rare. Here we study repulsively interacting Bose gases at and near a quantum critical point, and find evidences that such strongly correlated gases obey simple non-mutual FES over a wide range of interaction strengths in both one and two dimensions. Based on exact solutions in one dimension, quantum Monte Carlo simulations and experiments in both dim...

We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported by recent experiments and can be proven in Boltzmann regime. It implies a universal form for the grand potential which is characterized by only a few universal numbers in degenerate limit. This universal form provides a simple way to determ...

Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of the cluster expansion. Assuming a certain scaling of the single-particle partition functions, relevant to systems of noninteracting particles with various dispersion laws, both in a box and in an external harmonic potential, we derive a uni...

I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusion statistics) through one-dimensional (1D) channels. Observing that the particle, energy, entropy and heat fluxes through the 1D channel are similar to the particle, internal energy, entropy and heat capacity of a quantum gas in a two-dimensional (2D) flat box, respectively, I write analytical expressions for the fluxes at arbitrary temperatures. Using these expressions, I show th...

We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in some approximation, e.g. like Bose-Einstein condensates in magnetic traps. The numerical effort of our computation scheme grows only linear with the number of particles. As an example we calculate the relative ground state fluctuations and ...