Universal characteristics of nonuniform quasi-two-dimensional cold atom systems

We study the nonuniform potential effect in a quasi--two-dimensional (2D) Bose gas system at a finite temperature by numerically solving the projected Gross-Pitaevskii equation. The gradual emergence of superfluidity is confirmed by calculating the moment of inertia as the temperature decreases. Reflecting the nonuniformity of the system, the long-distance decay of a phase-correlation function is characterized by a local effective exponent, $\ensuremath{\eta}(r)$, which depends on the local superfluid density. This ``local-density approximation'' is endorsed by the 2D Gaussian field theory with the nonuniform coupling constant. Indeed, the effective exponent turns out to be close to $1/4$ at the boundary of the phase-coherent region.