Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

We investigate systems of interacting bosonic particles confined within slablike boxes of size L2×Z with ZL, at their three-dimensional (3D) Bose-Einstein-condensation (BEC) transition temperature Tc, and below Tc where they experience a quasi-two-dimensional (quasi-2D) Berezinskii-Kosterlitz-Thouless (BKT) transition (at TBKT<Tc depending on the thickness Z). The low-temperature phase below TBKT shows quasi-long-range order: the planar correlations decay algebraically as predicted by the 2D spin-wave theory. This dimensional crossover, from a 3D behavior for TTc to a quasi-2D critical behavior for TTBKT, can be described by a transverse finite-size scaling limit in a slab geometry. Numerical evidence of the 3D→2D dimensional crossover is presented for the Bose-Hubbard model defined in anisotropic L2×Z lattices with ZL. We extend this scaling analysis to the case the slab geometry of the gas is effectively realized by a transverse (inhomogeneous) harmonic trap. Finally, we discuss off-equilibrium behaviors arising from slow time variations of the temperature across the BEC transition of gases confined within a slab geometry. We argue that the system develops an off-equilibrium transverse finite-size scaling under these time-dependent protocols.