Renormalized Calculation of Phonon Damping in Quantum Crystals

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Abstract
We derive the imaginary part of the phonon self-energy to lowest order in frequency and temperature in terms of effective anharmonic interactions which are determined by higher order elastic constants. Since our results are derived to all orders in the bare anharmonic interactions they can be applied to quantum crystals. Comparing with renormalization theory we give a new interpretation of the "elastic-continuum model" for crystals and the "quantum-hydrodynamic model" for He II.