Energy Spectrum of Lattices with Defects. I : General Theory

概要

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An attempt is presented for calculating the spectrum of the vibrational frequencies as well as that of electronic energy levels of crystal lattices with defects. It is shown that the Fourier or the Laplace transform of the spectrum can be obtained from the trace of density matrices which satisfy a set of simultaneous differential-difference equations. Formal solutions of these equations are given, which are analogous to the integral expressions for additive functions of normal mode frequencies originally used by Montroll and Potts. As another approach to the solution of the equations, the perturbation expansion method is employed, which yields a cluster expansion or an expansion in terms of the concentration of defects. Finally the moment method and its correspondence to the random walk problem are discussed.
理論物理学刊行会の論文
1961-01-25