Thermodynamics of a free SUq(2) fermionic system

Abstract

We calculate the partition function, average occupation number and internal energy for a SU q (2) fermionic system and compare this model at T = 0 with the ordinary fermionic, q = 1, case. At low temperatures and q ≫ 1 we find the chemical potential µ to have the same temperature dependence than the Fermi case. For q ≪ 1, the function µ(T ) has in addition a linear dependence on T

Bose-Einstein condensation of a quantum group boson gas

“…This same feature was also found at low temperatures for the case of a quantum group fermion gas [5]. Then, the interactions introduced by the SU q (2) symmetry are such that they decrease the entropy below the one corresponding to the standard case q = 1.…”

“…As it is well known, in the quantum inverse scattering method and vertex models, the parameter q acquires a physical meaning through its relation with Planck's constant and the anisotropy of the lattice respectively. In order to look for the physical role that q could play in other areas of physics, in previous papers [5,6] we began a study of the thermodynamic properties of quantum group gases, which are the quantum group fermion (QGF) and quantum group boson (QGB) models. These models can be interpreted as either fermion or boson gases with interactions fixed by the quantum group.…”

Chiral symmetry restoration and pion properties in a q-deformed NJL model

“…The q-deformed fermionic algebra [7] that we shall use is based in the work of Ubriaco [8], where the thermodynamic properties of a many fermion system were studied. In the construction of a q-covariant form of the BCS approximation [9], it was shown that the creation and annihilation operators of the su q (2 j + 1) fermionic algebra are given by…”

Effect of quantum group invariance on trapped Fermi gases

“…In this model, Bose-Einstein condensation is realized as a second order phase transition, and the heat capacity becomes discontinuous at the critical temperature in one, two and three dimensions, even without the presence of an external potential. In a similar fashion, one can define [14] a set of operators Ψ i and Ψ i , with corresponding quantum group covariant algebraic relations, such that for q = 1 they become standard fermionic operators.…”

“…In Reference [14] we introduced a set of operators Ψ i that transform under SU q (2) and become ordinary fermions ψ i in the q → 1 limit. This is accomplished by the set of…”