Journal ArticleDOI
The Dynamics of a Disordered Linear Chain
TLDR
In this paper, the distribution function of the frequencies of normal modes of vibration of a disordered chain of one-dimensional harmonic oscillators is calculated analytically, in the limit when the chain becomes infinitely long.Abstract:
By a disordered chain we mean a chain of one-dimensional harmonic oscillators, each coupled to its nearest neighbors by harmonic forces, the inertia of each oscillator and the strength of each coupling being a random variable with a known statistical distribution law. A method is presented for calculating exactly the distribution-function of the frequencies of normal modes of vibration of such a chain, in the limit when the chain becomes infinitely long. For some special examples, in which the distribution law of the oscillator parameters is assumed to be of exponential form, the frequency spectra are calculated analytically. The theory applies equally well to a chain of masses connected by elastic springs and making mechanical vibrations, or to an electrical transmission line composed of alternating inductances and capacitances with random characteristics.read more
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Journal ArticleDOI
Freeman John Dyson. 15 December 1923—28 February 2020
TL;DR: Dyson was a Fellow of the Royal Society for 67 years, 11 months and 7 days, a record exceeded among the Society's scientific Fellows only by Sir Hans Sloane (elected 1685, Fellow for 67, 11, 20, and 20 days), Sir John Davis (elected 1822), Fellow for 68 years and 7 months, and possibly by Jean Chardellou (elected 1702), who is believed to have died aged 107 in 1771, but the precise date is unknown as discussed by the authors .
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Спектр поглощения одномерной цепочки с экситоном Френкеля при диагональном беспорядке в виде гиперболических дефектов@@@Absorption spectrum of one-dimensional chain with Frenkel's exiton under diagonal disorder represented by hyperbolic defects
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Calculation of the spectral dependence of the Anderson localization criterion in a one-dimensional system with correlated diagonal disorder
TL;DR: In this article, the authors considered the problem of calculating the Anderson criterion for a one-dimensional disordered chain with correlated disorder and solved this problem by the perturbation method with the inverse correlation length as the small parameter, and showed that the degree of localization not only naturally decreases but its spectral dependence also differs significantly from the spectral dependence in uncorrelated chains.
Journal ArticleDOI
Dynamics of disordered lattices
TL;DR: In the past ten years, numerous techniques have been applied to the study of simple models of disordered systems in attempts to understand the nature and effects of the lattice vibrations in real non-periodic structures.
Journal ArticleDOI
Stochastic approach to electron lattice system in one dimension
A. Holz,K.H. Bennemann +1 more
TL;DR: In this article, the one dimensional electron lattice problem is studied using Dyson's approach to 1D glasses, and an exact solution is found for the extreme narrow band case for the case of a single electron.