A remark about internal Lifshitz asymptotes
type: Item
instance of: scholarly article
title: A remark about internal Lifshitz asymptotes
zbMATH Open document ID: 1003.60063
DOI: 10.1016/S1631-073X(02)02415-9
author: Frédéric Klopp
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-01-09T00:00:00Z
review text: Let \(H_\omega =H+V_\omega\) be a random operator acting on \(L^2(\mathbb R^d)\) where \(H\) is a \(\mathbb Z^d\)-periodic Schrödinger operator, \(V_\omega (x)=\sum_{\gamma \in \mathbb Z^d}\omega_\gamma V(x- \gamma)\), \(\omega_\gamma\) are i.i.d. bounded nonnegative random variables, \(V(x)\geq 0\) has a power-like decay at infinity. The author studies the asymptotic behavior of the integrated density of states \(N_p(E)\) of the operator \(H_\omega\), as \(E\to +0\). The crucial quantity is the number \[ \kappa =-\lim\limits_{E\to +0}\frac{\log |\log \mathbb P\{ \omega_0\leq E\}|}{\log E}. \] Depending on the value of \(\kappa\), the asymptotics of \(N_p(E)\) is different, being interpreted as a representation of the classical or quantum regime.
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 47B80
zbMATH DE Number: 1777371
zbMATH Keywords: random Schrödinger operator
zbMATH Keywords: integrated density of states
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
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full work available at URL: s1631-073x(02)02415-9
OpenAlex ID: W2078861156
description: scientific article; zbMATH DE number 1777371