ν-Dimensional ideal quantum q-gas: Bose-Einstein condensation and λ-point transition

The authors consider an ideal quantum q-gas in ν spatial dimensions and energy spectrum ωi αpα. Departing from the Hamiltonian H = ω[N], the authors study the effect of the deformation on thermodynamic functions and equation of state of that system. The virial expansion is obtained for the high temperature (or low density) regime. The critical temperature is higher than in non-deformed ideal gases. They show that Bose-Einstein condensation always exists (unless when ν/α = 1) for finite q but not for q = ∞. Employing numerical calculations and selecting for ν/α the values 3/2, 2 and 3, the authors show the critical temperature as a function of q, the specific heat CV and the chemical potential μ as functions of T/Tcq for q = 1.05 and q= 4.5. CV exhibits a λ-point discontinuity in all cases, instead of the cusp singularity found in the usual ideal gas. The results indicate that physical systems which have quantum symmetries can exhibit Bose-Einstein condensation phenomenon, the critical temperature being favored by the deformation parameter