Asymptotics of a time-splitting scheme for the random Schrödinger equation with long-range correlations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1307.65009
author: Christophe Gomez
author: Olivier Pinaud
publication date: 2014-08-22T00:00:00Z
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35Q41
zbMATH DE Number: 6333651
zbMATH Keywords: random Schrödinger equation
zbMATH Keywords: long-range correlations
zbMATH Keywords: high frequency asymptotics
zbMATH Keywords: splitting scheme
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1051/m2an/2013113
OpenAlex ID: W2071352137
DOI: 10.1051/M2AN/2013113
title: Asymptotics of a time-splitting scheme for the random Schrödinger equation with long-range correlations
published in: European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
review text: A time-splitting scheme for the Schrödinger equation with random potential with long-range correlation is considered. The time-splitting is straightforward, separating the Laplacian and the potential.NEWLINENEWLINEThe high-frequency limit of the given equation is known to exhibit three distinct regimes depending on the scaling of the equation. It is shown that in a statistical sense, the time-splitting shows the correct asymptotic behaviour in all three regimes for a timestep independent of the frequency parameter. This is because the commutator between Laplacian and potential is small in a statistical sense. In contrast, much more stringent conditions apply if pathwise convergence is required.
reviewed by: Philipp Dörsek
description: scientific article; zbMATH DE number 6333651