CALCULATIONS OF THE VIBRATIONAL SPECTRA OF DISORDERED SYSTEMS I. VIBRATIONAL SPECTRUM OF A ONE-DIMENSIONAL CHAIN WITH RANDOMLY DISTRIBUTED IMPURITY SPRINGS II. THE ELASTIC SPECTRA OF TWO-DIMENSIONAL DISORDERED LATTICES

摘要

The frequency spectrum of a one-dimensional lattice containing randomly distributed impurity springs has been evaluated to first order in the concentration, q, of impurity springs. It is shown that, with some mathematical manipulation, the solution can be placed into correspondence with the solution of Langer for the analogous problem of isotopic impurities.