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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Journal ArticleDOI
Dynamics of an ion chain in a harmonic potential.
Giovanna Morigi,Shmuel Fishman +1 more
TL;DR: These results reproduce with good approximation the dynamics of chains consisting of dozens of ions and determine the critical transverse frequency required for the stability of the linear structure, found to be in agreement with results obtained by different theoretical methods.
Journal ArticleDOI
A record-driven growth process
C. Godreche,J.M. Luck +1 more
TL;DR: A novel stochastic growth process, the record-driven Growth process, which originates from the analysis of a class of growing networks in a universal limiting regime, and exhibits temporal self-similarity in the late-time regime.
Journal ArticleDOI
The relaxation-time spectrum of diffusion in a one-dimensional random medium: an exactly solvable case
TL;DR: In this article, an analytical expression for the density of states ρ(e) (inverse relaxation time spectrum) is derived for the average probability of return at any time at zero energy ρ (e) exhibits a variety of singular behaviours with a continuously varying exponent.
Journal ArticleDOI
Lyapunov exponents of large, sparse random matrices and the problem of directed polymers with complex random weights
J. Cook,Bernard Derrida +1 more
TL;DR: An analytic expression is given for the largest Lyapunov exponent of products of random sparse matrices, with random elements located at random positions in the matrix, through an analogy with the problem of random directed polymers on a Cayley tree.
Journal ArticleDOI
The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity
TL;DR: In this article, the Iwasawa decomposition of random real 2×2 matrices is used to identify a continuum regime where the mean values and the covariances of the three Iwasava parameters are simultaneously small, and the Lyapunov exponent of the product is assumed a scaling form.