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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

High temperature behavior of a two-parameter deformed quantum group fermion gas

Abdullah Algin, Metin Arık, Ali Serdar Arıkan

Published Jan 24, 2002• 49 citations
Publisher

Abstract

We discuss a two-parameter deformed quantum group fermion gas with SU(q/p)(2) symmetry. In order to obtain the role of the deformation parameters (q,p) on the thermodynamics of the system, we calculate several thermodynamical functions and investigate the high temperature behavior of a SU(q/p)(2) fermion gas through a SU(q/p)(2)-invariant fermionic Hamiltonian. However, the ordinary fermion gas results can be obtained by applying the limit q=p=1.

DOI
10.1103/physreve.65.026140

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We discuss a two-parameter deformed quantum group fermion gas with SU(q/p)(2) symmetry. In order to obtain the role of the deformation parameters (q,p) on the thermodynamics of the system, we calculate several thermodynamical functions and investigate the high temperature behavior of a SU(q/p)(2) fermion gas through a SU(q/p)(2)-invariant fermionic Hamiltonian. However, the ordinary fermion gas results can be obtained by applying the limit q=p=1.
We investigate the low temperature behaviour of a two-parameter generalized bosonic quantum gas with -symmetry, where q 1 and q 2 are real independent deformation parameters. We calculate, in the thermodynamical limit, several statistical and thermodynamical functions of the system through an -invariant bosonic Hamiltonian. In the low and high temperature limits, the specific heat of the system is obtained in terms of some functions of the deformation parameters q 1 and q 2 . At the critical temperature being higher than that of the free boson gas, the specific heat of the two-parameter generalized boson gas exhibits a λ-point transition behaviour. We also discuss the conditions under which the Bose–Einstein condensation would occur in the present two-parameter generalized boson model. However, the free boson gas results can be recovered in the limit q 1 = q 2 = 1.
We consider the simplest SU q(2) invariant fermionic Hamiltonian and calculate the low and high temperature behavior for the two distinct cases q>1 and q<1. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to q≠1. At high temperatures we find that the sign of the second virial coefficient depends on q, and vanishes at q=1.96. An important consequence of this fact is that the parameter q connects the fermionic and bosonic regions, showing therefore that SU q(2) fermions exhibit fractional statistics in three spatial dimensions.
We consider the simplest SUq(2) invariant fermionic hamiltonian and calculate the low and high temperature behavior for the two distinct cases q> 1 and q < 1. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to q ̸ = 1. At high temperatures we find that the sign of the second virial coefficient depends on q, and vanishes at q = 1.96. An important consequence of this fact is that the parameter q connects the fermionic and bosonic regions, showing therefore that SUq(2) fermions exhibit fractional statistics in three spatial dimensions.
We discuss the role that quantum group symmetries, in particular SUq(2)SU_q(2)SUq​(2), play in a thermodynamic system at high temperatures. We show that the interactions introduced by the quantum group symmetries, are such that a quantum group gas describe repulsive and attractive behavior in two and three spatial dimensions.
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.
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.