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
More filters
Journal ArticleDOI
Frequency filtering in disordered granular chains
Brian P. Lawney,Stefan Luding +1 more
TL;DR: In this article, disorder-induced frequency filtering is studied for one-dimensional systems composed of random, pre-stressed masses interacting through both linear and nonlinear (Hertzian) repulsive forces.
Journal ArticleDOI
Dynamical aspects of disorder in condensed matter
TL;DR: In this paper, the most relevant experimental methods are reviewed, as well as recent advances in computer simulation, which is becoming increasingly important in this field, and examples of recent applications of these techniques to study the various aspects of dynamical disorder are provided.
Journal ArticleDOI
Strange attractors in disordered systems
G Gyorgyi,Pál Ruján +1 more
TL;DR: In this paper, the presence of fractal-type stationary probability densities, including the density of the local field, is demonstrated on the typical example of the one-dimensional Ising model with discrete randomness.
Posted Content
Operator and entanglement growth in non-thermalizing systems: many-body localization and the random singlet phase
TL;DR: In this article, the authors characterize the growth and spreading of operators and entanglement in two paradigmatic non-thermalizing phases (the many-body localized phase and the random singlet phase) using out-of-time-ordered correlators, the entangler contour, and operator entenglement measures.