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Lifshitz singularities in the total and the wavenumber-dependent spectral density of random harmonic chains

โœ Scribed by Th.M. Nieuwenhuizen; J.M. Luck


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
969 KB
Volume
145
Category
Article
ISSN
0378-4371

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โœฆ Synopsis


Lifshitz has shown that the density of states of random systems becomes exponentially small near the band edge. We perform a detailed computation in a one-dimensional system and calculate the periodic prefactor of this essential singularity. The analysis is extended to the wavenumberdependent spectral density. The periodic amplitude is derived for the exactly soluble cases, where the distribution of masses is exponential. For binary distributions the leading behavior in the concentration of light masses is also derived.


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