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

✍ 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
• DOI: 10.1016/0378-4371(87)90245-7

✦ 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.