Phase Space Density

From Qwiki

Phase-space density $ρ$ in a harmonic trap is traditionally expressed as

$\rho = N\left(\frac{\hbar\bar{\omega}}{k_b T}\right)^3$

Where $N$ is atom number, $\bar{\omega}$ is mean trap frequency, $T$ is the kinetic temperature, $k b$ is Boltzmann's constant, and $\hbar$ is Dirac's constant,

Bose-Einstein condensation (BEC) in a single species traditionally occurs at a critical temperature $T c$ such that $\rho=\zeta(3)\simeq 1.202$ , where $ζ$ is the Riemann zeta function.