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Some considerations on the phonon theory of second sound Adams, David Kendall

Abstract

In investigating the propagation of second sound in a gas of non-interacting phonons, this thesis employs a field theoretical description of the quantized pressure excitations in liquid helium II, as first presented by R. Kronig and A, Thellung. The relations derived by these writers are generalized with a Galileo transformation. Also, the assumption is made that the phonons obey a Bose-Einstein distribution and the resulting expressions compared with those obtained intuitively in the earlier investigations of H. Kramers, Several serious disagreements are found between these two approaches to the problem. The most serious of which is the lack of a plane wave solution for the set of equations describing a phonon gas under a small temperature disturbance. This is a result that is unexpected in a first order second sound calculation and at present appears as a weakness in the Kronig and Thellung formulation.

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