Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate

We investigate some aspects of the Bose-Einstein condensation (BEC) of quantum gases in the presence of inhomogeneous conditions. We consider three-dimensional (3D) quantum gases trapped by an external potential when the temperature is sufficiently low to show a BEC phase region around the center of the trap. If the trap is sufficiently large, different phases may coexist in different space regions, when moving from the center of the trap. We show that the quantum gas develops a peculiar critical behavior at the boundary of the BEC region, whose scaling behavior is controlled by the universality class of the homogenous BEC transition. We provide numerical evidence of this phenomenon, for lattice atomic gases modeled by the 3D Bose-Hubbard Hamiltonian.