A note on the symplectic integration of the nonlinear Schrödinger equation

Clemens Heitzinger; Christian Ringhofer

doi:10.1023/B:JCEL.0000029454.06133.f9

A note on the symplectic integration of the nonlinear Schrödinger equation

Clemens Heitzinger, Christian Ringhofer

Mathematical and Statistical Sciences, School of (SoMSS)

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

8 Scopus citations

Abstract

Numerically solving the nonlinear Schrödinger equation and being able to treat arbitrary space dependent potentials permits many application in the realm of quantum mechanics. The long-term stability of a numerical method and its conservation properties is an important feature since it assures that the underlying physics of the solution are respected and it ensures that the numerical result is correct also for small time spans. In this paper we describe symplectic integrators for the nonlinear Schrödinger equation with arbitrary potentials and perform numerical experiments comparing different approaches and highlighting their respective advantages and disadvantages.

Original language	English (US)
Pages (from-to)	33-44
Number of pages	12
Journal	Journal of Computational Electronics
Volume	3
Issue number	1
DOIs	https://doi.org/10.1023/B:JCEL.0000029454.06133.f9
State	Published - 2004

Keywords

Difference methods
Nonlinear Schrödinger equations
Symplectic integration

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Modeling and Simulation
Electrical and Electronic Engineering

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10.1023/B:JCEL.0000029454.06133.f9

Cite this

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title = "A note on the symplectic integration of the nonlinear Schr{\"o}dinger equation",

abstract = "Numerically solving the nonlinear Schr{\"o}dinger equation and being able to treat arbitrary space dependent potentials permits many application in the realm of quantum mechanics. The long-term stability of a numerical method and its conservation properties is an important feature since it assures that the underlying physics of the solution are respected and it ensures that the numerical result is correct also for small time spans. In this paper we describe symplectic integrators for the nonlinear Schr{\"o}dinger equation with arbitrary potentials and perform numerical experiments comparing different approaches and highlighting their respective advantages and disadvantages.",

keywords = "Difference methods, Nonlinear Schr{\"o}dinger equations, Symplectic integration",

author = "Clemens Heitzinger and Christian Ringhofer",

note = "Funding Information: The first author acknowledges support by the Austrian Science Fund (Fonds zur F{\"o}rderung der wissenschaft-lichen Forschung, FWF) via an Erwin Schr{\"o}dinger Fellowship.",

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T1 - A note on the symplectic integration of the nonlinear Schrödinger equation

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AU - Ringhofer, Christian

N1 - Funding Information: The first author acknowledges support by the Austrian Science Fund (Fonds zur Förderung der wissenschaft-lichen Forschung, FWF) via an Erwin Schrödinger Fellowship.

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Y1 - 2004

N2 - Numerically solving the nonlinear Schrödinger equation and being able to treat arbitrary space dependent potentials permits many application in the realm of quantum mechanics. The long-term stability of a numerical method and its conservation properties is an important feature since it assures that the underlying physics of the solution are respected and it ensures that the numerical result is correct also for small time spans. In this paper we describe symplectic integrators for the nonlinear Schrödinger equation with arbitrary potentials and perform numerical experiments comparing different approaches and highlighting their respective advantages and disadvantages.

AB - Numerically solving the nonlinear Schrödinger equation and being able to treat arbitrary space dependent potentials permits many application in the realm of quantum mechanics. The long-term stability of a numerical method and its conservation properties is an important feature since it assures that the underlying physics of the solution are respected and it ensures that the numerical result is correct also for small time spans. In this paper we describe symplectic integrators for the nonlinear Schrödinger equation with arbitrary potentials and perform numerical experiments comparing different approaches and highlighting their respective advantages and disadvantages.

KW - Difference methods

KW - Nonlinear Schrödinger equations

KW - Symplectic integration

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A note on the symplectic integration of the nonlinear Schrödinger equation

Abstract

Keywords

ASJC Scopus subject areas

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