Intermittent lower bound on quantum diffusion
type: Item
instance of: scholarly article
title: Intermittent lower bound on quantum diffusion
zbMATH Open document ID: 1001.81019
DOI: 10.1023/A:1007610717491
author: Italo Guarneri
author: Hermann Schulz-Baldes
published in: Letters in Mathematical Physics
publication date: 2002-07-08T00:00:00Z
review text: Let \(H\) be a self-adjoint, bounded Hamiltonian acting on the Hilbert space \(\ell^2(\mathbb{N})\). The canonical base is denoted by \((|n \rangle)_{n \in\mathbb{N}}\). The unbounded position operator on \(\ell^2(\mathbb{N})\) is defined by \(X|n\rangle=n|n\rangle\). The authors are interested in studying the spreading of a wave packet initially localized at \(|0 \rangle\) under the quantum dynamics generated by \(H\), and analyze it with help of the moments of the time-averaged probability distribution on \(\mathbb{N}\), notably the time-averaged expectation values of powers of \(X\). The authors' goal is to characterize the spreading by properties of the spectral measure \(\mu\) of \(H\) with respect to \(|0\rangle\).
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1441358
zbMATH Keywords: quantum dynamics
zbMATH Keywords: self-adjoint bounded Hamiltonian
zbMATH Keywords: spreading of a wave packet
zbMATH Keywords: spectral measure
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1007610717491
OpenAlex ID: W1601195999
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description: scientific article; zbMATH DE number 1441358