Bose-Einstein condensation (BEC) of a noninteracting Bose gas of N particles in a two-dimensional box with Dirichlet boundary conditions is studied. Confirming previous work, we find that BEC occurs at finite N at low temperatures T without the occurrence of a phase transition. The conventionally-defined transition temperature TE for an infinite 3D system is shown to correspond in a 2D system with finite N to a crossover temperature between a slow and rapid increase in the fractional boson occupation N0/N of the ground state with decreasing T. We further show that TE ~ 1/log(N) at fixed area per boson, so in the thermodynamic limit there is no significant BEC in 2D at finite T. Thus, paradoxically, BEC only occurs in 2D at finite N with no phase transition associated with it. Calculations of thermodynamic properties versus T and area A are presented, including Helmholtz free energy, entropy S , pressure p, ratio of p to the energy density U/A, heat capacity at constant volume (area) CV and at constant pressure Cp, isothermal compressibility kappa_T and thermal expansion coefficient alpha_p, obtained using both the grand canonical ensemble (GCE) and canonical ensemble (CE) formalisms. The GCE formalism gives acceptable predictions for S, p, p/(U/A), kappa_T and alpha_p at large N, T and A, but fails for smaller values of these three parameters for which BEC becomes significant, whereas the CE formalism gives accurate results for all thermodynamic properties of finite systems even at low T and/or A where BEC occurs.
The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: large deviations
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础科学研究所国际理论科学中心）；LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学法国国家科学研究中心理论与物质物理实验室）；Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589（索邦大学法国国家科学研究中心高能理论与物理实验室）
Observing Properties of an Interacting Homogeneous Bose--Einstein Condensate: Heisenberg-Limited Momentum Spread, Interaction Energy and Free-Expansion Dynamics
Universal critical behavior in ideal Bose-Einstein condensation
Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Institut für Angewandte Physik, Universität Bonn（波恩大学应用物理研究所）；Kirchhoff-Institut für Physik, Universität Heidelberg（海德堡大学基希霍夫物理研究所）
