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
Lattice dynamics of ordered and disordered Cu3 Au with a tight-binding potential model
Fabrizio Cleri,Vittorio Rosato +1 more
TL;DR: In this paper, the phonon dispersion curves for both ordered and configurationally disordered cubic phases of Cu3Au are calculated using force constants derived from a many-body tight-binding potential.
Journal ArticleDOI
Some problems in the theory of a sturm-liouville equation
B M Levitan,I S Sargsyan +1 more
TL;DR: In this article, the authors considered the convergence and summability of eigenfunction expansions for unboundedly increasing potential, and established the convergence of expansions and differentiated expansions in eigenfunctions in an ordinary and generalised Fourier integral.
Posted Content
Zeta function for the Lyapunov exponent of a product of random matrices
Ronnie Mainieri,Ronnie Mainieri +1 more
TL;DR: In this paper, a cycle expansion for the Lyapunov exponent of a product of random matrices is derived, which is non-perturbative and numerically effective, which allows the Lipschitz exponent to be computed to high accuracy.
Journal ArticleDOI
Disorder-induced Purcell enhancement in nanoparticle chains
TL;DR: In this paper, the authors reported on numerical study of plasmonic nanoparticle chains with long-range dipole-dipole interaction and showed that the introduction of positional disorder gives a peak in the density of resonant states (DOS) at the frequency of individual nanoparticle resonance.
Journal ArticleDOI
Weak Disorder Expansion of Liapunov Exponents in a Degenerate Case
N. Zanon,Bernard Derrida +1 more
TL;DR: In this paper, the weak disorder expansion of the Liapunov exponents of a product of random matrices can be derived when the unperturbed matrices have two degenerate eigenvalues.