Bose-Einstein condensation of a quantum group boson gas

Abstract

We study the Bose-Einstein condensation of a gas with SU q (2) symmetry. We show, in the thermodynamic limit, that the boson interactions introduced by the quantum group symmetries enhance Bose-Einstein condensation giving a discontinuity in the heat capacity C v at the critical temperature T c . The critical temperature and the gap in C v increase with the value of the parameter q and become approximately constant for q > 3. PACS number(s):

Fibonacci oscillators and two-parameter generalized thermostatistics

“…Also, the virial coefficients in (23) are different from the results of the one-and two-parameter deformed SU q ð2Þ-covariant boson gas models [19][20][21][22][39][40][41]. We should note that all the high-temperature thermostatistical functions given in (11)-(23) reduce to the undeformed boson gas functions in the limit q 1 ¼ q 2 ¼ 1.…”

Effect of quantum group invariance on trapped Fermi gases

“…In contrast to the fermion case, where µ is constant for D = 1, the function µ(q < 1) decreases with T . Figure 1 shows a graph of the chemical potential for q = 0.2, 1, 2, obtained from a numerical calculation of Equation (12). The chemical potential at zero temperature, µ 0 (q), is independent of D for q > 1.…”

“…In the quantum inverse scattering method the parameter q acquires a physical meaning through its relation with the Planck's constant. In two recent articles [12,13] we considered the system represented by the hamiltonian…”

Thermodynamics of two-parameter quantum group Bose and Fermi gases

“…After the promoting studies of Ubriaco [1][2][3][4] related with the high and low temperature behaviour of the one-parameter deformed quantum group SU q (2)-invariant bosonic and fermionic gases, two-parameter generalizations of these works have recently been developed [5][6][7][8][9][10][11]. In particular, the generalizations in [5][6][7][8][9][10] contain quantum group bosonic as well as fermionic gas structures, whose particle algebras under consideration are invariant under the two-parameter deformed quantum group SU r (2) with r = p/q where p = q, (p, q) ∈ R + .…”