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
Spectral properties and scaling relations in off diagonally disordered chains
J. E. Ure,N. Majlis +1 more
TL;DR: In this paper, the authors obtained the localization length of an off-diagonally disordered chain as a function of the energy and disorder width of the chain, and used it in the Herbert-Spencer-Thouless formula for localization.
Journal ArticleDOI
Entanglement entropy distribution in the strongly disordered one-dimensional Anderson mode
B. Friedman,R. Berkovits +1 more
Journal ArticleDOI
Ballistic Heat Conduction and Mass Disorder in One Dimension
Zhun-Yong Ong,Gang Zhang +1 more
TL;DR: In this paper, the authors show that there exists a critical crossover length scale below which ballistic heat conduction can coexist with mass disorder, where the thermal conductivity scales asymptotically with the chain length.
Phase transitions and multifractal properties of random field Ising models
TL;DR: In this article, the authors considered random field Ising models with quenched dichotomous symmetric random field on the Bethe lattice and proved the properties of the multifractal spectrum of this effective field.