Debye Model - Extension To Other Quasi-particles

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.

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    We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.
    Blaise Pascal (1623–1662)