CANONICAL BOSE-EINSTEIN CONDENSATION IN A PARABOLIC WELL

The Bose-Einstein condensation is investigated for N particles in a pa rabolic confining potential. The partition function in the grand-canon ical as well as in the canonical ensemble is obtained analytically, an d the thermodynamical quantities are studied for the one-dimensional ( 1D) and for the three-dimensional (3D) version of the model. In 1D, a dramatic rise in the ground state occupancy with decreasing temperatur e is predicted. Both the grand-canonical and the canonical ensemble yi eld the same behavior of the specific heat as a function of the temper ature and the number of particles. There is no indication of a critica l phenomenon for a finite number of particles, neither in the ground s tate occupancy nor in the specific heat. Also in 3D, both ensembles gi ve an identical contribution for the specific heat, but showing thereb y a phase transition with a critical temperature which scales with the cube root of the number of particles, as predicted before by semi-cla ssical continuum models. Copyright (C) 1996 Elsevier Science Ltd