Does the Phonon Spectrum in Superfluid 4He Curve Upward?
There has recently been some controversy about the shape of the spectrum of phonons in superfluid 4He.1 In this note we use the theory of canonical transformations to demonstrate that the spectrum must be concave at low momenta. It is shown that if the spectrum were convex, there could be no three-phonon vertex in the interaction; a fortiori, there can be no three-phonon process in the attenuation of sound. However, the experimental dependence2 of the attenuation on frequency and temperature is clearly that of a three-phonon process. Hence the spectrum must be concave.
KeywordsMatrix Element Canonical Transformation Phonon Spectrum Energy Shell Quasiparticle Energy
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