Density of States in Aperiodic Solids

概要

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Some fundamental questions concerning densities of states for dynamical systems in aperiodic solids are discussed by way of three examples : (1) Harmonic vibrations in a binary alloy, (2) Impurity scattering of electrons due to short range forces, (3) Virtual localized states near the Fermi level in a metal. The "Friedel sum rule"which connects the density of states in a disturbed system and that in an undisturbed one in terms of the sum of all scattering phase shifts is studied with each example to see how the latter quantities accumulate to produce an extensive nature inherent to that notion to be given to an infinite, thermodynamically stable system. (A kind of spatial fluctuation-dissipation theorem.) Requirements are deduced for the function, analytic as a function of the complex energy variable, whose boundary values on the real axis yield the density of states. It is based on Wigner's R-function which Wigner introduced in connection with nuclear scattering studies many years ago. The CPA theory-its approximation formula to compute the function (which we systematically derive here) - is re-examined from this point of view and is shown to meet such requirements.
理論物理学刊行会の論文
1974-01-10