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
From disordered quantum walk to physics of off-diagonal disorder
Qifang Zhao,Jiangbin Gong +1 more
TL;DR: In this paper, the authors studied disordered discrete-time quantum walk in a finite chain, where the diagonal disorder can be set to zero by construction. And they showed that the dynamics of the quantum walk with disorder manifest all the main features of off-diagonal disorder.
Journal ArticleDOI
Dynamics of Ising spin glasses far below the lower critical dimension: the one-dimensional case and small clusters
J. D. Reger,Kurt Binder +1 more
TL;DR: In this article, the Glauber model is studied for symmetric distributions (±J and gaussian) of the nearest-neighbour interactionJ, including a magnetic field, and the complex magnetic susceptibility χ(ω) and the time-dependent remanent magnetizationm(t) are found exactly for given bond configurations {Jij} by diagonalization of the Liouville operator.
Journal ArticleDOI
Exactly soluble diluted random one-dimensional lattices
TL;DR: In this article, exact solutions for the characteristic function, which determines the density of states and inverse localization length, and one-particle Green function are presented for a class of lattice models with diluted randomness.
Journal ArticleDOI
Transmission Properties of an Isotopically Disordered One‐Dimensional Harmonic Crystal
TL;DR: In this paper, the amplitude SN(ω) of a wave of frequency ω which is transmitted by a disordered array of N isotopic defects in a one-dimensional crystal has been investigated in the limit in which N → ∞ while the over-all concentration of the defects in the array remains fixed.
Journal ArticleDOI
Vibrational frequency spectrum of random crystal lattices
TL;DR: In this paper, the moments of the vibrational frequency spectrum associated with a three-dimensional, two-component, random lattice were estimated from its zeroth through eighteenth order moments.