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
More filters
Journal ArticleDOI
1/f noise and spectral singularities in strongly disordered electronic systems
TL;DR: In this paper, the authors discuss the common origin of 1/f noise in the power spectrum of random walks in a random environment and the 1/E-like spectral anomaly for tight-binding electronic systems with off-diagonal disorder.
Journal ArticleDOI
On the Theory of the Phonon Component of Disjoining Pressure of Thin Liquid Films
Journal ArticleDOI
Commensurability effects in one-dimensional Anderson localization: anomalies in eigenfunction statistics
TL;DR: In this paper, the authors developed a regular approach to anomalous statistics of normalized eigenfunctions at such commensurability points, which is based on an exact integral transfer-matrix equation for a generating function, where the descender of the generating function is the distribution function of phase which determines the Lyapunov exponent and the local density of states.
Posted Content
Rigidity of the three-dimensional hierarchical Coulomb gas
TL;DR: In this article, the hierarchical Coulomb gas was shown to be hyperuniform at both macroscopic and microscopic scales, with upper and lower bounds for the order of fluctuations that match up to logarithmic factors.