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
Order-disorder phenomenon in sodium nitrate studied by low-frequency Raman scattering
TL;DR: In this article, the low-frequency Raman spectrum of a single crystal of NaN${O}}_{3}$ has been measured for temperatures from 25 to 300\ifmmode^\circ\else\text degree\fi{}C covering both ordered and disordered phases.
Journal ArticleDOI
Universal distribution of Lyapunov exponents for products of Ginibre matrices
TL;DR: In this paper, the authors derived the Lyapunov exponents for an infinite product and showed that for a large number of product matrices, the distribution of each Lyunov exponent is normal and compute its $t$-dependent variance as well as corrections in a 1/t$ expansion.
Journal ArticleDOI
Simple random matrix model for the vibrational spectrum of structural glasses
TL;DR: In this paper, the authors study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network coordination, and find that the low frequency vibrational modes in structural glasses have three regimes: a very low-frequency regime that can be predicted analytically using extremal statistics, an intermediate regime with quasilocalized modes, and a plateau in
Journal ArticleDOI
On the Melting of Copolymeric DNA
TL;DR: A result is that the breadth of the transition is a function of the base composition, and the predicted broadening with available experimental data is excellent for DNA from simple organisms which probably possess only one kind of DNA molecule each.
Journal ArticleDOI
Effets isotopiques et propriétés thermodynamiques en phase condensée. II
Ilya Prigogine,Jean Jeener +1 more
TL;DR: In this paper, the authors extended the method developed in a recent paper by the authors and R. Bingen to real three dimensional lattices, and the zero point energy was calculated for isotopic mixtures and pure isotopes.