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
Posted Content
Poisson statistics of eigenvalues in the hierarchical Dyson model
TL;DR: In this article, the authors considered the hierarchical Laplacian of the Poisson point process and derived the total variation convergence rate for the poisson approximation under some natural assumptions.
Journal ArticleDOI
Mesoscopic fluctuations of the density of states and conductivity in the middle of the band for disordered lattices
TL;DR: In this article, the mesoscopic properties of two-dimensional lattices with randomly distributed substitutional impurities are studied. And the correlations of the levels lying on opposite sides of the Fermi surface, due to nesting, are investigated.
Journal ArticleDOI
Zero mode protection at particle-hole symmetry: a geometric interpretation
TL;DR: In this article, the properties of zero modes in particle-hole symmetric systems are analyzed in the presence of strong random scattering by a disordered environment based on the calculation of the time-averaged density distribution on a lattice.
Journal ArticleDOI
An alternative approach to the normal frequencies of a randomly disordered linear chain
TL;DR: In this paper, an attempt is made to gain some insight into the statistical character of the normal frequencies of a long chain of harmonic oscillators with randomly disordered masses, where the size of the randomness in each of the masses tends to 0 like L−1/2.
Journal ArticleDOI
Universal scaling near the band edge for one-dimensional disordered systems
TL;DR: In this article, the integrated spectral density and the localisation length of one-dimensional tight-binding models with weak diagonal and off-diagonal disorder were analyzed. And the scaling law near the band edge is satisfied for all kinds of disorder and its simple analytical derivation is given in terms of 'annealed' or 'effective medium' approximations.