# Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations

Christophe Gomez; Olivier Pinaud

- Volume: 48, Issue: 2, page 411-431
- ISSN: 0764-583X

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topGomez, Christophe, and Pinaud, Olivier. "Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.2 (2014): 411-431. <http://eudml.org/doc/273181>.

@article{Gomez2014,

abstract = {This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial condition, and the statistical properties of the random medium. We show that the splitting scheme captures these regimes in a statistical sense for a time stepsize independent of the frequency.},

author = {Gomez, Christophe, Pinaud, Olivier},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {random Schrödinger equation; long-range correlations; high frequency asymptotics; splitting scheme},

language = {eng},

number = {2},

pages = {411-431},

publisher = {EDP-Sciences},

title = {Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations},

url = {http://eudml.org/doc/273181},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Gomez, Christophe

AU - Pinaud, Olivier

TI - Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 2

SP - 411

EP - 431

AB - This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial condition, and the statistical properties of the random medium. We show that the splitting scheme captures these regimes in a statistical sense for a time stepsize independent of the frequency.

LA - eng

KW - random Schrödinger equation; long-range correlations; high frequency asymptotics; splitting scheme

UR - http://eudml.org/doc/273181

ER -

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