Localization for discrete one-dimensional random word models☆
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TLDR
In this article, the authors consider Schrodinger operators in l2(Z) whose potentials are obtained by randomly concatenating words from an underlying set W according to some probability measure ν on W. They prove spectral localization and, away from a finite set of exceptional energies, dynamical localization for such models.About:
This article is published in Journal of Functional Analysis.The article was published on 2004-03-15 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Random function & Random element.read more
Citations
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Delocalization in Random Polymer Models
TL;DR: In this paper, it was shown that the Lyapunov exponent vanishes quadratically at a generic critical energy and that the density of states is positive there, and the level spacing is shown to be regular at the critical energy.
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Power-law bounds on transfer matrices and quantum dynamics in one dimension–II
TL;DR: In this article, quantum dynamical lower bounds for a number of discrete one-dimensional Schrodinger operators are derived from power-law upper bounds on the norms of transfer matrices.
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Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices
TL;DR: In this paper, a method for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix is presented.
Journal ArticleDOI
Upper bounds on wavepacket spreading for random Jacobi matrices
TL;DR: In this paper, a method for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix is presented.
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Dependence of the Density of States on the Probability Distribution for Discrete Random Schrödinger Operators
TL;DR: In this paper, it was shown that the density of states measure for random Schrödinger operators on the Bethe lattice is weak Hölder-continuous in the probability measure.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
An Introduction to Ergodic Theory
TL;DR: The first part of the text as discussed by the authors provides an introduction to ergodic theory suitable for readers knowing basic measure theory, including recurrence properties, mixing properties, the Birkhoff Ergodic theorem, isomorphism, and entropy theory.
Book
Jacobi Operators and Completely Integrable Nonlinear Lattices
TL;DR: In this paper, the Toda system and the Kac-van Moerbeke system are studied. But the initial value problem is not considered in this paper, as it is in the case of Jacobi operators with periodic coefficients.