On the relaxation rate spectrum of phonons

The nature of the spectrum of the normal processes collision operator for phonons is studied in the framework of the theory of Hilbert space. It is shown that in the limit V to infinity the continuous part of the spectrum extends down to the value zero. A rigorous proof regarding the absolutely continuous part of the spectrum of the collision operator in the gas model approximation is given. The only eigenvalue is zero and the continuum covers the range (0, infinity ).