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The European Physical Journal B

Particle density and transition temperature of weakly interacting quantum gases

Renu Bala, Sunita Srivastava, K. N. Pathak

Published Oct 1, 2015• 3 citations
Publisher
DOI
10.1140/epjb/e2015-60365-1

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We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for dipoles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem that claims the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical temperature (up to 10nK10\phantom{\rule{0.16em}{0ex}}\mathrm{nK}10nK at realistic densities). This opens wide possibilities for the studies of the superfluid regime in weakly interacting Fermi gases, which has not been observed so far.
Abstract We study thermodynamic properties of weakly interacting Bose gases above the transition temperature of Bose–Einstein condensation in the framework of a thermodynamic perturbation theory. Cases of local and non-local interactions between particles are analyzed both analytically and numerically. We obtain and compare the temperature dependencies for the chemical potential, entropy, pressure, and specific heat to those of noninteracting gases. The results set reliable benchmarks for thermodynamic characteristics and their asymptotic behavior in dilute atomic and molecular Bose gases above the transition temperature.
We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.