Bose-Einstein Condensate

Physics: BEC: macroscopic occupation of ground state when nλ_dB³ ≥ 2.612. Critical temperature T_c = (ℏ²/mk_B)·(n/ζ(3/2))^(2/3) ≈ 100–500 nK for alkali atoms. Condensate fraction N₀/N = 1−(T/T_c)³ in harmonic trap. Gross-Pitaevskii equation: iℏ∂ψ/∂t = [−ℏ²∇²/2m + V + g|ψ|²]ψ; g = 4πℏ²a/m (a = scattering length). Thomas-Fermi regime: kinetic energy negligible → inverted parabola density profile. First BEC: Cornell-Wieman 1995 (⁸⁷Rb, ~2000 atoms), Ketterle 1995 (Na), Nobel 2001. Superfluidity: persistent currents, quantized vortices (ℏ/m per vortex).