Localisation of phonons

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Abstract
A careful computer simulation of two- and three-dimensional, isotopically disordered harmonic crystals is presented. The problem is classical and it is argued that ideas of percolation theory suffice to explain the existence of a mobility edge in three dimensions whenever the heavier masses, but not the lighter ones, percolate. No other mobility edges are found. At the mobility edge the density of states vanishes. In addition, a modified inverse participation ratio (IPR) is discussed which appropriately handles resonances.