What is between Fermi-Dirac and Bose-Einstein Statistics?

Once again the possibility of the existence of particle statistics intermediate between those of Fermi-Dirac and Bose-Einstein surfaces. Here attention is drawn to the fact that some fifteen years ago it was shown that such so-called 'intermediate' statistics correspond to no physical process and the stationary probability distributions of intermediate statistics are not compatible with any mechanism which allows a variation between Fermi-Dirac and Bose-Einstein statistics.

Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the fundamental ensembles of statistical physics avoiding any limiting procedures, quantum hypothesis and even statistical entropy maximization. This point of view leads also to some related classes of correlated particle statistics.

An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model ...

Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q = 1 and q -> infinity (n_i/q -> 1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclus...

In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the thermodynamic quantity which can simultaneously describe both gas phase and condensed phase is solved with the help of the homogeneous Riemann-Hilbert problem, so one can judge whether there exists a phase transition and determine the phase...

In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as $a^{\dagger}b=\Lambda\left(N\right) $ or $N=\Lambda^{-1} \left( a^{\dagger}b\right)$, where $N$, $a^{\dagger}$, and $b$ denote the number, creation, and annihilation o...

In this study, The particles of the quantum gases, namely bosons and fermions are regarded as g-ons by the paremeter of the fractional exclusion statistics g. With this point of departure, the distribution function of the g-on gas is obtained by the variational, steepest descent and statistical methods. The distribution functions which are found by means of these three methods are compared. It is seen that the thermostatistical formulations of the quantum gases can be unified...

In this paper, we show two kinds of entangled many body systems with special statistic properties. Firstly, an entangled fermions system with a pairwise entanglement between every two particles in the lowest energy energy level obeys the fractional statistics. As a check, for particle number N=2, N=3 and N=4, considering that any two fermions in the lowest Landau level are entangled in a proper way, the Laughlin wave function can be derived. The results reveals the explicit e...

I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are pr...

This article gives a detailed presentation of the authors' recent results on the ground state properties of the Bose gas. It is a much expanded version of a talk given by one of the authors (E.H.L.) at the conference "Perspectives in Analysis" at the KTH, Stockholm, June 23, 2003. It is based on, but supersedes, the article math-ph/0204027.