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Imagine a cavity in a infinitely extended solid filled with another type of solid in thermal equilibrium. Are there statistics for phonons equivalent to the Black Body Radiation by Planck?

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    $\begingroup$ Essentially yes. Thinking of black body radiation as thermal excitations of an electromagnetic field, the analogue for phonons would be thermal excitations of a deformation field (see Debye theory). One subtlety is that for certain solids, small thermal forces can produce large local deformations, which can change the density of states significantly. $\endgroup$ – TotallyRhombus Aug 9 '15 at 12:01
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    $\begingroup$ Basically, yes. The main difference is that there is a minimum wavelength (maximum frequency) for phonons but not for photons. Also, phonons have a non-linear dispersion relation, which means the density of states does some weird things. $\endgroup$ – lnmaurer Aug 10 '15 at 16:07

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