Bose-Fermi Variational Theory of the Bose-Einstein Condensate Crossover to the Tonks Gas

Abstract
A number-conserving hybrid Bose-Fermi variational theory is developed and applied to investigation of the Bose-Einstein condensate crossover to the Tonks gas in toroidal and long cylindrical traps of high aspect ratio, where strong many-body correlations and condensate depletion occur.