Bose-Einstein condensates at equilibrium inside a pancake-shaped trap:   dimensional cross-over in the scattering properties
  Two-dimensionality of the scattering events in a Bose-Einstein condensate introduces a logarithmic dependence on density in the coupling constant entering a mean-field theory of the equilibrium density profile, which becomes dominant as the s-wave scattering length gets larger than the condensate thickness. We analyze quantitatively the role of the form of the coupling constant in determining the transverse profile of a condensate confined in a harmonic pancake-shaped trap at zero temperature. We trace the regions of experimentally accessible system parameters for which the cross-over between different dimensionality behaviors may become observable through in situ imaging of the condensed cloud with varying trap anisotropy and scattering length. 
B. Tanatar (1) A. Minguzzi (2), P. Vignolo (2)and M.P. Tosi (2) ((1)   Bilkent University, Ankara; (2) SNS, Pisa)