Finite-size effects on the Bose-Einstein condensation critical   temperature in a harmonic trap
  We obtain second and higher order corrections to the shift of the Bose-Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections. 
Jos\'e M. B. Noronha
cond-mat.quant-gas quant-ph