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

We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E49, 5103 (1994)] as a generalization of the Pauli exclusion principle, which is based on a proper definition of the transition probability between two states, we derive a variety of different statistical distributions interpolating between bosons and fermions. The Hal...

An interpolation between the canonical partition functions of Bose, Fermi and Maxwell-Boltzmann statistics is proposed. This interpolation makes use of the properties of Jack polynomials and leads to a physically appealing interpolation between the statistical weights of the three statistics. This, in turn, can be used to define a new exclusion statistics in the spirit of the work of Haldane.

This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -- namely, the fraction of particles in the ground state and the specific heat -- are calculated here exactly in terms of temperature and fugacity. These calculations are complemented by a numerical calculation of fugacity in terms of the number of particles, without tak...

We discuss the thermodynamics of a gas of free particles obeying Haldane's exclusion statistics, deriving low temperature and low density expansions. For gases with a constant density of states, we derive an exact equation of state and find that temperature-dependent quantities are independent of the statistics parameter.

At the end of 2017, an interdisciplinary scientific seminar was organized at Moscow University, devoted to the study and development of a new scientific concept created by V.P. Maslov, allowing you to take a fresh look at the statistics of Bose-Einstein and Fermi-Dirac ideal gases. This new point of view allows us to interpret the indicated statistics as particular cases of statistical properties in number theory, on the one hand, and to indicate the limits of phase transitio...

Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles where any of them can be a fermion with probability [P] and can be a boson with probability [1-P]?. In this paper this question is solved

We give two formulations of exclusion statistics (ES) using a variable number of bosonic or fermionic single-particle states which depend on the number of particles in the system. Associated bosonic and fermionic ES parameters are introduced and are discussed for FQHE quasiparticles, anyons in the lowest Landau level and for the Calogero-Sutherland model. In the latter case, only one family of solutions is emphasized to be sufficient to recover ES; appropriate families are sp...

The aim of this Tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term {\it cold} implies that considered temperatures are low, such that quantum theory is necessary, even if temperatures are finite. And the term {\it atoms} means that the considered particles are structureless, being defined by their masses and mutual interactions. Atoms are {\it trapped} in the sense that they form a...

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...

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pau...