Crossover from one to three dimensions for a gas of hard-core bosons
  We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultra-cold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the full 1D regime for suitable transverse confinement. 
Kunal K. Das, M.D. Girardeau and E.M. Wright