Assuming the dispersion relation (omega=A k^{mathcal{s}}), where (omega) is the angular frequency and (k) the wave number
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Assuming the dispersion relation \(\omega=A k^{\mathcal{s}}\), where \(\omega\) is the angular frequency and \(k\) the wave number of a vibrational mode existing in a solid, show that the respective contribution toward the specific heat of the solid at low temperatures is proportional to \(T^{3 / s}\).
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