Special energies and special frequencies
type: Item
instance of: scholarly article
title: Special energies and special frequencies
zbMATH Open document ID: 0618.60059
DOI: 10.1007/BF01214419
author: M. Endrullis
author: H. Englisch
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: ''Special frequencies'' have been asserted to be zeros of the density of frequencies corresponding to a random chain of coupled oscillators. Our investigation includes both this model and the random one-dimensional Schrödinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lifšic asymptotic of the integrated density of states k(E) at special energies \(E_ s\), which is not only of the classical type \(\exp (-c/| E-E_ s|^{1/2})\) but also \(\exp (-c'/| E-E_ s|)\) is a typical behaviour. In addition, other asymptotics occur, e.g. \(| E-E_ s|^{c''}\), which show that k(E) need not be \(C^{\infty}\).
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4003184
zbMATH Keywords: random chain of coupled oscillators
zbMATH Keywords: Schrödinger operator
MaRDI profile type: Publication
cites work: Q4066072
cites work: One-dimensional Schrödinger operators with ergodic potential
cites work: SPECTRA OF RANDOM SELF ADJOINT OPERATORS
cites work: On the density of states of Schrodinger operators with a random potential
cites work: The phase formalism for one-dimensional random Schrödinger operators
cites work: Functional Equations for the Vibrational Spectra of Diatomic Chains
cites work: Infinite representability of Schrödinger operators with ergodic potential
cites work: On the spectrum of Schrödinger operators with a random potential
cites work: Almost periodic Schrödinger operators. II: The integrated density of states
cites work: Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
cites work: Bounds on the Ljapunov Exponent
cites work: Q4185363
cites work: An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
cites work: Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model
description: scientific article; zbMATH DE number 4003184