Pseudofermion approach to binary disordered systems. II. Goldstone systems with off-diagonal disorder

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Abstract
A simple approximation is developed for the frequency spectrum of binary disordered Goldstone systems such as phonons in mixed crystals with both mass and force-constant disorder. This localized pseudofermion approximation is a simplification of the one-pseudofermion approximation previously discussed, which gives the coherent-potential approximation for systems with diagonal disorder. The approximation is shown to give properly analytic Green's functions, and to have the correct virtual-crystal, atomic, and dilute limits. Numerical results are presented for linear chains of atoms for comparison with the exact density of states, and results are given in the random-hopping electronic model for comparison with the theory of Blackman et al. It is found that the theory produces results very similar to those produced by the coherent-potential approximation for diagonal disorder. However, the neglect of pseudofermion propagation and certain overlap effects leads to somewhat incorrect locations of the impurity band edges. This effect vanishes when the disordered force constants superimpose linearly.