Sound velocity and dimensional crossover in a superfluid Fermi gas in an   optical lattice
  We study the sound velocity in cubic and non-cubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothened by interactions and eventually vanishes when interactions are strong enough. For non-cubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the 1D and 2D limits. 
T. Koponen, J.-P. Martikainen, J. Kinnunen, and P. Torma