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Journal of Physics Conference Series

General thermostatistical properties of a q -deformed fermion gas in two dimensions

Abdullah Algin, Mustafa Şenay

Published Oct 1, 2016• 9 citations
Publisher

Abstract

Starting with a deformed fermionic grand partition function, we study the high and low temperature thermostatistical properties of a special q -deformed fermion gas in two spatial dimensions. Many of the deformed thermostatistical functions such as the specific heat and the entropy are derived in terms of the real deformation parameter q for the range q < 1. For high temperatures, we specifically focus on the behavior of both the entropy function and the deformed virial coefficients in the equation of state for the q -fermion gas in two dimensions. Possible physical applications of the present q -fermion gas are briefly discussed.

DOI
10.1088/1742-6596/766/1/012008

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Starting with a deformed fermionic grand partition function, we study the high and low temperature thermostatistical properties of a special q -deformed fermion gas in two spatial dimensions. Many of the deformed thermostatistical functions such as the specific heat and the entropy are derived in terms of the real deformation parameter q for the range q < 1. For high temperatures, we specifically focus on the behavior of both the entropy function and the deformed virial coefficients in the equation of state for the q -fermion gas in two dimensions. Possible physical applications of the present q -fermion gas are briefly discussed.
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.
It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.
We study the high-temperature behavior of an intermediate-statistics fermionic gas model whose quantum statistical properties enable us to effectively deduce the details about both the interaction among deformed (quasi)particles and their anyonic behavior. Starting with a deformed fermionic grand partition function, we calculate, in the thermodynamical limit, several thermostatistical functions of the model such as the internal energy and the entropy by means of a formalism of the fermionic q calculus. For high temperatures, a virial expansion of the equation of state for the system is obtained in two and three dimensions and the first five virial coefficients are derived in terms of the model deformation parameter q. From the results obtained by the effect of fermionic deformation, it is found that the model parameter q interpolates completely between bosonlike and fermionic systems via the behaviors of the third and fifth virial coefficients in both two and three spatial dimensions and in addition it characterizes effectively the interaction among quasifermions. Our results reveal that the present deformed (quasi)fermion model could be very efficient and effective in accounting for the nonlinear behaviors in interacting composite particle systems.
It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.
A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose–Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range [Formula: see text]. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.