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
Theories of electrons in one-dimensional disordered systems
Paul Erdos,Roy C. Herndon +1 more
TL;DR: A critical survey of the literature on the theory of electronic states in, and electron transmission through, models of one-dimensional disordered solids and liquids is given in the first part.
Journal ArticleDOI
Classical diffusion of a particle in a one-dimensional random force field
TL;DR: In this paper, a comprehensive study of the motion of a damped Brownian particle evolving in a static, one dimensional Gaussian random force field is presented, and the full asymptotic probability distributions (averaged over disorder) are precisely determined, in terms of Levy stable laws.
Journal ArticleDOI
Electronic Transport in DNA
TL;DR: It is found that random and lambda-DNA have localization lengths allowing for electron motion among a few dozen basepairs only, and a novel enhancement of localization lengths is observed at particular energies for an increasing binary backbone disorder.
Journal ArticleDOI
Density of states from moments. Application to the impurity band
TL;DR: The moments of the electronic density of states of a disordered system described by a tight binding model can be directly computed as a function of the overlap integrals and the local order of the system as discussed by the authors.
Journal ArticleDOI
Electronic energy-levels in dense plasmas
TL;DR: In this article, a simple parameterization of pressure ionization, discussed limitations of the Debye-Huckel model for plasma perturbations, and survey an approximate description of X-ray spectra based on the WKB approximation.