Bose-Einstein Condensation
Macroscopic ground-state occupation in the ideal Bose gas
Controls
Temperature T/T_c
0.80
Total particles N
1000
Energy levels shown
20
T_c = —
N₀/N = —
N₀ = —
Critical temperature:
T_c = (2πℏ²/mk_B)·(n/ζ(3/2))^(2/3)
Below T_c, condensate fraction:
N₀/N = 1 − (T/T_c)³
The ground state (ε=0) accumulates macroscopic occupation. Above T_c, distribution follows Bose-Einstein statistics with μ→0.