Weak localization and anharmonicity of phonons

作者: E. Akkermans , R. Maynard

DOI: 10.1103/PHYSREVB.32.7850

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摘要: The problem of localization phonons in disordered materials is studied the framework weak-localization theory. Quantum correction to phonon diffusion calculated by resummation technique maximally crossed diagrams two and three dimensions. strong energy dependence elastic mean free path\char22{}the Rayleigh-Klemens scattering\char22{}is responsible for existence a threshold frequency ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$ where constant vanishes. value depends only on local fluctuation masses Debye This describes phenomenon density fluctuations or second sound. self-energies are strongly affected this quantum via anharmonic interactions. basic couplings contribute one-phonon renormalization provide shortening lifetime as well excess spectral vicinity threshold. In dimensions, electrons, dynamical diverges logarithmically when goes zero. A procedure convergence used cutting off low-frequency contributions at inelastic relaxation rate. Renormalization obtained self-consistent way. Finally tentative application previous results low-temperature properties glasses discussed. particular plateau thermal conductivity accompanied specific heat all measured so far could be understood manifestation acoustic-phonon critical ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$. .AE

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