Abstract
We investigate the absorption of infra-red radiation by an impure ionic crystal, due to coupling with phonon modes. By means of a standard diagrammatic perturbation theory, the phonon Green's function and hence the infra-red spectrum is calculated. The two absorption peaks corresponding to longitudinal and transverse modes are broadened by disorder into bands of finite width. This behaviour is very similar to that of electrons in a dirty metal with a magnetic field, with the phonon modes playing a similar role to the Landau levels of the electrons. This suggests that the diagrammatic formalism can be used to study the transport properties of phonons in a crystal with impurities and long-ranged dipole-dipole interactions, by analogy with the methods used in the transport theory of electrons in disordered metals.
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