On the Vibration of Disordered Linear Lattice. III
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Eigenfrequency spectrum of isotopic two-component disordered lattice has been calculated approximately by a method which requires only a comparatively small amount of numerical work. An argument based on perturbation theory shows formally that the spectrum of completely random lattice is the same as that of virtual regular lattice composed of atoms with average mass, except at the edge and outside of the band. We have first investigated how far this statement is valid and obtained the result that the smaller the concentration of lighter atoms, the larger the frequency domain in which the spectrum can be regarded as approximately the same as that of virtual regular lattice. Next, we have calculated the spectrum in the neighborhood of the edge of the band where the above statement does not hold, by applying the moment-trace method only to that region. The result is that when the concentration of lighter atoms is comparable with or larger than that of heavier atoms, there is only one presumably rounded maximum at the position of the band-edge of virtual regular lattice, whereas when the number of lighter atom becomes smaller, there appears an impurity band, its separation from the main band coming out the more distinct, as the concentration of lighter atoms gets smaller. Both results are natural provided the spectrum is to approach that of Poisson lattice as the lighter atoms become few.
- 理論物理学刊行会の論文
- 1960-03-25
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