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
Spectral Statistics in Chiral-Orthogonal Disordered Systems
TL;DR: In this paper, the singularities in the averaged density of states and the corresponding statistics of the energy levels in two-and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder, were described.
Journal ArticleDOI
Lifshitz tails and long-time decay in random systems with arbitrary disorder
TL;DR: In this article, the authors derived an asymptotic expansion of the Lifshitz tail to all orders in this logarithmic variable, for continuous distributions starting with a power law.
Journal ArticleDOI
On the remarkable spectrum of a non-Hermitian random matrix model
TL;DR: Using the Dyson?Schmidt equation, this paper showed that the spectrum of a non-denumerable set of lines in the complex plane is the support of a periodic Hamiltonian, obtained by the infinite repetition of any finite sequence of the disorder variables.
Journal ArticleDOI
Electronic energy transfer in an impurity band
Klaus Godzik,Joshua Jortner +1 more
TL;DR: In this article, the authors explore the dynamics of triplet electronic energy transfer in an impurity band of a substitutionally-disordered material, and derive approximate results for the average density of excitation within the framework of the pair-approximation.
Journal ArticleDOI
Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains.
Naomichi Hatano,Joshua Feinberg +1 more
TL;DR: The Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as a function of energy is studied and the only available efficient algorithm for finding the density of states of models with interactions is found.