Numerical simulation of the nonlinear schrödinger equation with multidimensional periodic potentials

Zhongyi Huang; Shi Jin; A. Peter Markowich

doi:10.1137/070699433

Numerical simulation of the nonlinear schrödinger equation with multidimensional periodic potentials

Zhongyi Huang^*, Shi Jin, A. Peter Markowich

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodingerequations subject to periodic and confining potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattic Bose-Einstein condensates in the superfluid regime.

Original language	English (US)
Pages (from-to)	539-564
Number of pages	26
Journal	Multiscale Modeling and Simulation
Volume	7
Issue number	2
DOIs	https://doi.org/10.1137/070699433
State	Published - 2008
Externally published	Yes

Keywords

Bloch decomposition
Bose
Einstein condensates
Fermi approximation
Lattice potential
Onlinear Schrodinger equation
Splitting spectral method
Thomas
time

ASJC Scopus subject areas

General Chemistry
Modeling and Simulation
Ecological Modeling
General Physics and Astronomy
Computer Science Applications

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10.1137/070699433

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title = "Numerical simulation of the nonlinear schr{\"o}dinger equation with multidimensional periodic potentials",

abstract = "By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodingerequations subject to periodic and confining potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattic Bose-Einstein condensates in the superfluid regime.",

keywords = "Bloch decomposition, Bose, Einstein condensates, Fermi approximation, Lattice potential, Onlinear Schrodinger equation, Splitting spectral method, Thomas, time",

author = "Zhongyi Huang and Shi Jin and Markowich, {A. Peter}",

year = "2008",

doi = "10.1137/070699433",

language = "English (US)",

volume = "7",

pages = "539--564",

journal = "Multiscale Modeling and Simulation",

issn = "1540-3459",

publisher = "Society for Industrial and Applied Mathematics",

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TY - JOUR

T1 - Numerical simulation of the nonlinear schrödinger equation with multidimensional periodic potentials

AU - Huang, Zhongyi

AU - Jin, Shi

AU - Markowich, A. Peter

PY - 2008

Y1 - 2008

N2 - By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodingerequations subject to periodic and confining potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattic Bose-Einstein condensates in the superfluid regime.

AB - By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodingerequations subject to periodic and confining potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattic Bose-Einstein condensates in the superfluid regime.

KW - Bloch decomposition

KW - Bose

KW - Einstein condensates

KW - Fermi approximation

KW - Lattice potential

KW - Onlinear Schrodinger equation

KW - Splitting spectral method

KW - Thomas

KW - time

UR - http://www.scopus.com/inward/record.url?scp=55149094759&partnerID=8YFLogxK

U2 - 10.1137/070699433

DO - 10.1137/070699433

M3 - Article

AN - SCOPUS:55149094759

SN - 1540-3459

VL - 7

SP - 539

EP - 564

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

IS - 2

ER -

Numerical simulation of the nonlinear schrödinger equation with multidimensional periodic potentials

Abstract

Keywords

ASJC Scopus subject areas

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