Nonperturbative Effects on T_c of Interacting Bose Gases in Power-Law Traps

TL;DR

This paper calculates how interactions affect the critical temperature of Bose gases in power-law traps, revealing both perturbative and nonperturbative contributions and how trap inhomogeneity suppresses critical fluctuations.

Contribution

It introduces a variational perturbation theory approach to quantify the nonperturbative effects on T_c in power-law traps, including a new term related to trap shape.

Findings

The shift in T_c includes both linear and nonperturbative terms.

Increased inhomogeneity reduces critical fluctuation effects.

The nonperturbative term scales with a^{2 eta} and depends on trap shape.

Abstract

The critical temperature T_c of an interacting Bose gas trapped in a general power-law potential V(x)=\sum_i U_i|x_i|^{p_i} is calculated with the help of variational perturbation theory. It is shown that the interaction-induced shift in T_c fulfills the relation (T_c-T_c^0)/T_c^0= D_1(eta)a + D'(eta)a^{2 eta}+ O(a^2) with T_c^0 the critical temperature of the trapped ideal gas, a the s-wave scattering length divided by the thermal wavelength at T_c, and eta=1/2+\sum_i 1/p_i the potential-shape parameter. The terms D_1(eta)a and D'(eta) a^{2 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 a^{2 eta} contribution is qualitatively explained in terms of the Ginzburg criterion.