= Bose condensation with power-law dispersion
{c}
{title2=$\epsilon=Ap^\alpha,\quad0<\alpha<d$}
For a homogeneous ideal gas in $d$ dimensions with $A,\alpha>0$, the <density of states> scales as $\epsilon^{d/\alpha-1}$. At limiting chemical potential zero, the <Bose-Einstein distribution> is proportional to $1/\epsilon$ near zero energy. The excited-particle integral is finite exactly when $d/\alpha>1$. Thus positive-temperature condensation at fixed nonzero density is possible precisely for $0<\alpha<d$. A nonconserved particle number, as for ordinary equilibrium photons, removes the fixed-number saturation mechanism even when the integral is finite.
Back to article page
