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
The random phase property and the Lyapunov Spectrum for disordered multi-channel systems
TL;DR: In this paper, a random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrodinger operators and full random matrix theory is advocated, and strong numerical evidence that it holds in the Anderson model of localization is provided.
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Non-Hermitian quasilocalization and ring attractor neural networks.
TL;DR: Roles that Anderson localization could be playing in neural networks are explored by focusing on "spatially structured" disorder in synaptic connectivity matrices, and principal eigenvectors of the LEGI ring attractor networks with structured nearest-neighbor disorder are "quasilocalized," even with fully dense inhibitory connections.
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Electronic states on a fractal : exact Green's-function renormalization approach
Journal ArticleDOI
Simulations of the Hubbard model
TL;DR: In this article, results of simulations of the Hubbard model of interacting electrons on a lattice are discussed, with a brief discussion of methodology and point out some of the outstanding problems.
Journal ArticleDOI
Lifshitz singularities in the total and the wavenumber-dependent spectral density of random harmonic chains
TL;DR: In this paper, a detailed computation in a one-dimensional system and calculate the periodic prefactor of the essential singularity of random systems is presented. But the analysis is extended to the wavenumber-dependent spectral density.