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Phonon dispersion relation

For two polarizations in area $A$ and $\omega=C|k|^\alpha$, counting <wavevector> states in a disk gives
$$
g(\omega)=\frac{A}{\pi\alpha C^{2/\alpha}}
\omega^{2/\alpha-1}.
$$

Density of states for a two-dimensional power-law phonon dispersion

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 35A / b / i / Solution

Density of states for a two-dimensional power-law phonon dispersion

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Density of states for a two-dimensional power-law phonon dispersion

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