SPECTRUM OF HARMONIC EXCITATIONS ON FRACTALS.

Abstract

The density of states and the nature of the eigenmodes of the vibrating d-dimensional Sierpinski gasket are investigated. The results hold for the tight-binding or any general quadratic Hamiltonian. For d greater than 1, the spectral measure is shown to be a superposition of two distinct pure point measures of relative weights d/(d plus 1) and 1/(d plus 1). The eigenmodes associated with each part are explicitly calculated.