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
Strong Disorder RG approach - a short review of recent developments
Ferenc Iglói,Cécile Monthus +1 more
TL;DR: The Strong Disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [Phys. Rep. 412, 277] as mentioned in this paper, and the aim of the present colloquium paper is to give an overview of these various recent developments.
Journal ArticleDOI
Functionals of the Brownian motion, localization and metric graphs
TL;DR: In this article, the spectral properties of the Schr\"odinger operator on graphs have been investigated in the context of a quantum particle coupled to the random magnetic field due to magnetic vortices, and the connection between spectral properties and winding functionals of the planar Brownian motion has been made.
Journal ArticleDOI
On Disordered One-dimensional Crystals
TL;DR: In this article, a mathematical method for the frequency distribution of disordered chains of atoms is presented, which leads in a direct manner both to an explicit expression for the spectrum distribution of a disordered chain of atoms and to a powerful technique for numerical evaluation of the spectrum.
Journal ArticleDOI
Lattice Vibration Spectra of Germanium-Silicon Alloys
TL;DR: In this paper, the infrared lattice absorption spectra of germanium-silicon alloys were determined in the wavelength region from 8-48 \ensuremath{\mu} and have been analyzed to obtain information on the lattice vibrational spectra.
Journal ArticleDOI
Calculation of regge poles by continued fractions - I
C. Lovelace,David R. Masson +1 more
TL;DR: In this paper, an expansion of the Regge trajectories for large energy is derived for singular and nonsingular potentials, and the Pade approximant is introduced in order to sum these asymptotic expansions.