λ- Transition to the Bose-Einstein Condensate

Abstract

We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statistics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of N atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discontinuous at the onset of condensation; the magnitude of the jump is about 6.6 Nk. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-N-corrections, and checked against numerical computations. © - Verlag der Zeitschrift für Naturforschung