= 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.
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