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
Citations
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Journal ArticleDOI
Lyapunov Exponents and Localization in Randomly Layered Media
John A. Scales,Erik S. Van Vleck +1 more
TL;DR: In this paper, the scaling effects of the heterogeneities on a propagating pulse can be characterized by the frequency-dependent localization length, i.e., the skin depth for multiple-scattering attenuation.
Journal ArticleDOI
Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder
TL;DR: In this paper, the authors studied the distribution of the n-th energy level for two different one-dimensional random potentials and showed that the distribution is related to the distance between two consecutive nodes of the wave function.
Journal ArticleDOI
Asymptotics of the distribution of the spectrum of random matrices
TL;DR: In this paper, a new inversion formula for the Stieltjes transforms of spectral functions of symmetric random matrices has been proposed, and the asymptotics of sums of smoothed densities of eigenvalue distributions of the distributions have been studied.
Journal ArticleDOI
Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains
TL;DR: In this paper, the integrated density of statesH(ω2) of a chain of harmonic oscillators with a binary random distribution of the masses was studied, and it was shown that there is a dense set of values of the squared frequency for which the difference H(ω 2+α)-H(α) has a singularity of the type ¦β¦2α, multiplied by a periodic function of ln ¦ ǫ 2α, where the exponent α and the period depend continuously on