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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Book ChapterDOI
Optical Properties of Nonmetallic Solids for Photon Energies below the Fundamental Band Gap
TL;DR: In this paper, the optical properties of solids in the infrared spectral region that are caused by interaction of electromagnetic radiation with lattice vibrations are discussed, and optical interactions in crystals resulting from one-phonon processes and multiphonon interactions are presented.
Journal ArticleDOI
Electronic Levels of a Model of Liquid Potassium
R Eisenschitz,P Dean +1 more
TL;DR: In this article, a one-dimensional model of a liquid is considered in which the distances of nearest neighbours are independent random variables having a given probability distribution Electronic levels are derived using the tight binding approximation.
Journal ArticleDOI
Spectral theory of random self-adjoint operators
TL;DR: A survey of spectral analysis of differential and finite-difference operators with random spatially homogeneous coefficients can be found in this paper, where the use of probabilistic ideas and methods now allows highly detailed spectral analysis to be performed for an essentially broader class of operators, as well as new problems and results obtained in the framework of this theory.
Journal ArticleDOI
Vibrational properties of hierarchical systems
TL;DR: In this article, the vibrational properties of one-dimensional hierarchical systems are investigated and results are obtained for both their eigenvalues and eigenvectors, and a connection is established between hierarchical vibration and diffusion problems, as well as to the same problems in random systems.
Journal ArticleDOI
Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid.
TL;DR: It is argued that a strong-disorder fixed point controls the low temperature susceptibility χ (T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0.