High-temperature behavior of a deformed Fermi gas obeying interpolating statistics

Abstract

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 whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.

Classical Model of Quons

“…However, it is easy to see that, although both of these formulations are equivalent for a( f ) = f , for another choice of a( f ) different from the identity, Equations (16) and (17) in general do not coincide.…”

“…Therefore, the study of physical systems that obey non-conventional statistics is one of the pillars of contemporary statistical physics [6][7][8][9][10][11][12]. Their interest spans from the theoretical foundation of generalized statistical mechanics [13,14], Fermi gas superfluid [15], high-temperature gas [16] and high-T c superconductivity [17], Laughlin particle with fractional charge related to fractional quantum Hall effect [18,19], Josephson junctions [20] and applications to quantum computation [21,22].…”

Fibonacci oscillators in the Landau diamagnetism problem

“…Thus, we will carry it out a Taylor expansion until second order of Eq. (25), which allows us the analysis of the insertion of the q-deformation. After performing some calculations we obtain…”

Couplingq-Deformed Dark Energy to Dark Matter

“…The -deformed scalar field is in fact a -deformed boson model, and the statistical mechanical studies ofdeformed boson models have shown that the pressure of the deformed bosons is generally negative. Not only do the 2 Advances in High Energy Physics different deformed boson models have a negative pressure, but also the different deformed fermion models can take negative pressure values [46][47][48][49][50]. Here, we consider thedeformed bosons and propose that the scalar field which is produced by these deformed bosons constitutes the dark energy in the universe.…”