PHYSICAL REVIEW A, vol.79, no.6, 2009 (SCI-Expanded)
Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the s-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that, for the case of a negative boson-fermion three-dimensional s-wave scattering length, the dimensional crossover stabilizes the mixture against collapse and drives it toward spatial demixing.