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
Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation
TL;DR: In this paper, the properties of the volume operator in loop quantum gravity were analyzed for the first time at generic vertices of valence greater than four, using a simplified formula for matrix elements derived in gr-qc/0405060.
Journal ArticleDOI
On the characteristic polynomials of Fibonacci chains
TL;DR: In this article, special diatomic linear chains with elastic nearest-neighbour interaction and the two masses distributed according to the binary Fibonacci sequence were studied, and the elastic nearest neighbor interaction was considered.
Journal ArticleDOI
Relaxation of magnetisation in one-dimensional random Glauber model
Deepak Kumar,J. Stein +1 more
TL;DR: In this article, numerical calculations for the relaxation of magnetisation in a one-dimensional random Glauber model are described for two probability distributions of the exchange constant, one allowing both the ferromagnetic and antiferromagnetic interactions, while the other only allowing only ferrommagnetic interactions.
Journal ArticleDOI
Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping
Akshay Krishna,Ravindra N. Bhatt +1 more
TL;DR: In this article, the authors studied the singular, but normalizable, distributions of hopping, whose behavior at small $t$ is of the form ρ 1/ [t \ln^{\lambda+1}(1/t) ], characterized by a single, continuously tunable parameter.
Journal ArticleDOI
Density of states and localization length in weakly disordered peierls chains
TL;DR: In this paper, the electron density of states and localization length for weakly disordered dimerized tight-binding chains are calculated for the continuum model with and without Gaussian disorder.