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
The solution to an inverse problem in stratified dielectric media
TL;DR: In this article, the average dielectric constant and thickness of the layers of a stratified DIMM were determined from measurements of transmitted power at a single frequency, where each sample of the medium that is available for measurement is modeled as a stack of layers of dielectrics of thicknesses li and K, and it is assumed that the li are identically distributed with some exponential distribution and that the K are identical distributed.
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Transport properties and density of states of quantum wires with off-diagonal disorder
TL;DR: In this paper, the random hopping problem in a quasi-one-dimensional geometry of N coupled chains (quantum wire with off-diagonal disorder) is reviewed, and the theory is compared to numerical simulations.
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Midgap states and generalized supersymmetry in semi-infinite nanowires
TL;DR: In this paper, the edge states of semi-infinite nanowires in the tight-binding limit are examined, and it is shown that these edge states occur within the gaps of the corresponding bulk spectrum (thus also called the midgap states).
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Random chains and complex transfer matrix attractors
TL;DR: In this article, the physical properties of one-dimensional disordered systems are obtained with a method which is a generalization of work by Schmidt and is carried out reformulating Schmidt's procedure in the language of non-linear processes and extending it to the complex plane.
Journal ArticleDOI
Effect of temporal noise on the single-electron transport in long molecules
TL;DR: In this article, the authors analyzed single-electron or exciton transport in long molecules in the presence of both static disorder and temporal noise both of which inevitably exist in biological systems.