An analysis of the effects of frequency crossing in the resonant scattering of thermal phonons

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Abstract
An analysis has been made of the change in thermal conductivity that occurs when the frequencies of two resonant phonon-scattering processes become equal, a situation which is termed a frequency crossing. The analysis is applicable when the effective width of the scattering processes is small compared with the spectral width of the thermal phonons. The frequency-crossing effect, which is an incoherent effect, is due to the non-linear relation between the strength of the scattering and the thermal conductivity, and can give rise to sharp changes in conductivity. Brief consideration is also given to analogous effects which are expected to occur in heat pulse work. A method is suggested for producing an amplitude-modulated component of narrow spectral width from a heat current, which might have application as a 'monochromatic' phonon source.