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
A calculation of cluster effects in disordered alloys
TL;DR: In this article, a general method of incorporating the effects of clusters of constituent atoms in the calculation of the excitation density of states in a disordered material is presented, where an unknown parameter is introduced into the logarithm of the secular determinant of the problem and subsequently determined self-consistently by minimizing approximately the interaction between clusters.
DissertationDOI
Quantum Phases and Phase Transitions In Disordered Low-Dimensional Systems: Thin Film Superconductors, Bilayer Two-dimensional Electron Systems, And One-dimensional Optical Lattices
TL;DR: In this article, it was shown that the experimentally observed lower-than-theory gap-Tc ratio in bilayer superconducting-normal-metal films is due to inhomogeneous couplings.
Journal ArticleDOI
Group ring elements with large spectral density
TL;DR: In particular, the best known upper bounds on mu((0,eps)) are not far from being optimal as mentioned in this paper, assuming that the Novikov-Shubin invariant of any such ring element is 0.
Journal ArticleDOI
Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder
TL;DR: In this article, the random hopping problem in a quasi-one-dimensional geometry of N coupled chains (quantum wire with off-diagonal disorder) is reviewed and compared to numerical simulations.
Journal ArticleDOI
Interferometric control of the photon-number distribution
H. Esat Kondakci,Alexander Szameit,Ayman F. Abouraddy,Demetrios N. Christodoulides,Bahaa E. A. Saleh +4 more
TL;DR: In this paper, the photon-number distribution is controlled by interfering two coherent beams within a disordered photonic lattice by sweeping a relative phase between two equal-amplitude coherent fields with Poissonian statistics that excite adjacent sites.