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
One dimensional X - Y model with random interaction constants
TL;DR: In this article, the excitation spectrum and free energy of a one dimensional X -Y model with random interaction constants were calculated, and the free energy was shown to be a function of the number of interaction constants.
Journal ArticleDOI
The superspin approach to a disordered quantum wire in the chiral-unitary symmetry class with an arbitrary number of channels
TL;DR: In this paper, a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product was used to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires perturbed by weak quenched disorder.
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Note on the low-frequency density of states for mass-disordered harmonic hamiltonians
TL;DR: In this article, simple bounds for the low-frequency density of state for mass-disordered harmonic systems are discussed for low-temperature specific heat and the temperature dependence of the low temperature specific heat is normal, of the Debye form.
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Application of Berezinskii's Diagram Method to Bond Disordered System with the Dimerization and the Staggered Field
Abstract: Based on the Berezinskii's diagram method, the density of states (DOS) of a bond disordered system has been calculated in the presence of the dimerization and the staggered field. It is found that the DOS near the center of the band behaves anomalously and that it is indicated that this feature is the cause of the coexistence phase of antiferromagnetism (AF) and dimerization in the disordered quasi-one-dimensional spin-Peierls (SP) system CuGe 1- y Si y O 3 .
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Many-body localization of zero modes
TL;DR: In this article, it was shown that analogous zero modes in interacting quantum systems can fully localize at sufficiently large disorder, but do so less strongly than nonzero modes, as signifed by their real-space and Fock-space localization characteristics.