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
Lattice topology dictates photon statistics.
TL;DR: In this article, it was shown that the photon statistics in ring lattices are determined by its parity, while the same quantities are insensitive to the parity of a linear lattice.
Journal ArticleDOI
Lattice vibrations of one-dimensional disordered systems
Shi-Yu Wu,S. P. Bowen,K. S. Dy +2 more
TL;DR: In this article, the effects of defects on the vibrational properties of solids is almost as old as the study of lattice dynamics in crystals, and because of the simplifying feature in the geometry of the crystalline solids, elegant theorems were developed so that the studies of normal modes and thermodynamic properties of disordered systems with periodic structures soon became the main stream of research.
Journal ArticleDOI
Spectral Dependence of the Degree of Localization in a 1D Disordered System with a Complex Structural Unit
TL;DR: In this paper, the spectral distribution of localisation in a 1D diagonally disordered chain of fragments, each of which consists of coupled two-level systems, was analyzed by means of developed perturbation theory for joint statistics of advanced and retarded Green's functions.
Journal ArticleDOI
Central peak in the density of states of a disordered linear chain
TL;DR: In this paper, the density of states of a one-dimensional tight-binding electron model with random hopping elements was studied, and it was proved that the single particle density near E = 0 as 1 |(E log 3 |E|)|.
Journal ArticleDOI
The eigenvalues of a randomly distributed matrix
TL;DR: In this article, a method based on the resolution of the symmetric matrix into two triangular ones is developed, which reduces the problem to a form which has the promise of being soluble by numerical methods.