Extension To Other Quasi-particles
For other bosonic quasi-particles, e.g., for magnons (quantized spin waves) in ferromagnets instead of the phonons (quantized sound waves) one easily derives analogous results. In this case at low frequencies one has different dispersion relations, e.g., in the case of magnons, instead of for phonons (with ). One also has different density of states (e.g., ). As a consequence, in ferromagnets one gets a magnon contribution to the heat capacity, which dominates at sufficiently low temperatures the phonon contribution, . In metals, in contrast, the main low-temperature contribution to the heat capacity, comes from the electrons. It is fermionic, and is calculated by different methods going back to Arnold Sommerfeld.
Read more about this topic: Debye Model
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