Theory of Defects in Quantum Crystals

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Abstract
The classical theory for mass defects in crystals is inapplicable to quantum crystals, where zero-point motion leads to a force-constant renormalization on the introduction of mass defects. We develop a variational theory for handling such problems which simplifies the renormalization so that the problem reduces to that of a single frequency-dependent mass defect, to be calculated in a self-consistent fashion. Various anomalies observed in the properties of quantum crystals are discussed in light of the present theory. The theory may also be used to calculate in a simple fashion the properties of extended defects in classical crystals.

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