Spectral Symmetry in Lattice Dynamical Models

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Abstract
Conditions are derived for the existence of symmetry in the squared frequency spectra of lattice dynamical models, and it is shown that the displacement eigenvectors associated with symmetrically related frequencies are simply related. It is also demonstrated that in some cases a delta function exists in the spectrum in addition to the symmetry related regions: the modes associated with the delta-function are vibrations in which certain atoms remain stationary. Various applications of the theory are discussed.

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