My talk will emphasize the fact that a phase transition in a finite
system is smooth --- rather than critical, as it is for the case of a
bulk system. This point will be illustrated using a simple
calculation that explores the onset of Bose-Einstein condensation in
one dimension. If time permits, I will discuss this problem in three
dimensions as well, both for free particles and for particles
confined to harmonic traps.
My talk will be based on several papers that I have
published in the Physical Review and in
the American Journal of Physics.