Nonperturbative Effects on Tc of Interacting Bose Gases in Power-Law Traps
Abstract
The critical temperature Tc of an interacting Bose gas trapped in a general power-law potential V(x)=Σi Ui|xi|pi is calculated with the help of variational perturbation theory. It is shown that the interaction-induced shift in Tc fulfills the relation (Tc-Tc0)/Tc0= D1(eta)a + D'(eta)a2 eta+ O(a2) with Tc0 the critical temperature of the trapped ideal gas, a the s-wave scattering length divided by the thermal wavelength at Tc, and eta=1/2+Σi 1/pi the potential-shape parameter. The terms D1(eta)a and D'(eta) a2 eta describe the leading-order perturbative and nonperturbative contributions to the critical temperature, respectively. This result quantitatively shows how an increasingly inhomogeneous potential suppresses the influence of critical fluctuations. The appearance of the a2 eta contribution is qualitatively explained in terms of the Ginzburg criterion.
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