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
Random-matrix theory of Majorana fermions and topological superconductors
TL;DR: In this paper, a review of the application of random-matrix theory in topological superconductors is presented, with a discussion of transport properties that are susceptible to the predicted existence of Majorana excitations in these exotic materials.
Journal ArticleDOI
Lyapounov exponent of the one dimensional Anderson model : weak disorder expansions
Bernard Derrida,E. Gardner +1 more
TL;DR: In this paper, the weak disorder expansion of the Lyapounov exponent y(E) of a discretized one-dimensional Schrodinger equation was analyzed and shown to be non-analytic at the band edge of the pure system.
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Exactly solvable model of electronic states in a three-dimensional disordered Hamiltonian: non-existence of localized states
TL;DR: In this paper, an exactly solvable model of a disordered Hamiltonian, valid in three dimensions, is presented, and the ensemble-averaged Green function, and hence the density of eigenstates, for the model are found exactly.
Journal ArticleDOI
Strong disorder RG approach of random systems
Ferenc Iglói,Cécile Monthus +1 more
TL;DR: In this paper, the authors describe the basic properties of infinite disorder fixed points, which are realized at critical points, and of strong disorder fixedpoints, which control the singular behaviors in the Griffiths-phases.
Journal ArticleDOI
The ergodic side of the many‐body localization transition
TL;DR: In this article, the ergodic phase of many-body localization (MBL) is considered and the available numerically exact and approximate methods for its study are discussed and a phenomenological explanation of its dynamical properties is presented.