= Bose-Einstein condensation temperature for an anisotropic effective mass
{c}
{title2=$k_BT_c=2\pi\hbar^2[n/(\sqrt\gamma\zeta(3/2))]^{2/3}/m$}
For a one-component ideal Bose gas with masses $(m,m,\gamma m)$, insert the <anisotropic ideal-gas density of states> in the excited-state number integral at chemical potential zero. The substitution $x=\varepsilon/(k_BT)$ gives $n=\sqrt\gamma(mk_BT/(2\pi\hbar^2))^{3/2}\zeta(3/2)$, which yields the displayed transition temperature. Thus at fixed density and the two lighter masses, $T_c\propto\gamma^{-1/3}$. This continuum ideal-gas result does not supply a finite-temperature transition for decoupled two-dimensional layers.
Back to article page
