Real-space condensation in a dilute Bose gas at low temperature
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/24816
Low Temperature Physics
- Research Paper 
We show with a direct numerical analysis that a dilute Bose gas in an external potential - which is chosen for simplicity as a radial parabolic well - undergoes at a certain temperature Tc a phase transition to a state supporting a macroscopic fraction of particles at the origin of the phase space (r=0, p=0). Quantization of particle motion in a well wipes out the sharp transition but supports a distribution of a radial particle density ρ(r) peaked at r=0 (a real-space condensate) as well as a phase-space Wigner distribution density W(r,p) peaked at r=0 and p=0 below a crossover temperature Tc* of order of Tc. A fixed-particle-number canonical ensemble, which is a combination of the fixed-N condensate part and the fixed-μ excitation part, is suggested to resolve the difficulty of large fluctuation of the particle number (δN∼N) in the Bose-Einstein condensation problem treated within the orthodox grand canonical ensemble formalism. © 2001 American Institute of Physics.