Explicit schemes for time propagating many-body wave functions

Autores
Frapiccini, Ana Laura; Hamido, Aliou; Schröter, Sebastian; Pyke, Dean; Mota Furtado, Francisca; O’Mahony, Patrick F.; Madroñero, Javier; Eiglsperger, Johannes; Piraux, Bernard
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrödinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.
Fil: Frapiccini, Ana Laura. Université Catholique de Louvain; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Fil: Hamido, Aliou. Université Catholique de Louvain; Bélgica
Fil: Schröter, Sebastian. Technische Universitat München; Alemania
Fil: Pyke, Dean. University of London; Reino Unido
Fil: Mota-Furtado, Francisca. University of London; Reino Unido
Fil: O’Mahony, Patrick F.. University of London; Reino Unido
Fil: Madroñero, Javier. Universidad del Valle; Colombia
Fil: Eiglsperger, Johannes. Numares GmbH; Alemania
Fil: Piraux, Bernard. Université Catholique de Louvain; Bélgica
Materia
TDSE
Explicit propagator
Arnoldi
Runge-Kutta
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/94789

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network_name_str CONICET Digital (CONICET)
spelling Explicit schemes for time propagating many-body wave functionsFrapiccini, Ana LauraHamido, AliouSchröter, SebastianPyke, DeanMota Furtado, FranciscaO’Mahony, Patrick F.Madroñero, JavierEiglsperger, JohannesPiraux, BernardTDSEExplicit propagatorArnoldiRunge-Kuttahttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrödinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.Fil: Frapiccini, Ana Laura. Université Catholique de Louvain; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Hamido, Aliou. Université Catholique de Louvain; BélgicaFil: Schröter, Sebastian. Technische Universitat München; AlemaniaFil: Pyke, Dean. University of London; Reino UnidoFil: Mota-Furtado, Francisca. University of London; Reino UnidoFil: O’Mahony, Patrick F.. University of London; Reino UnidoFil: Madroñero, Javier. Universidad del Valle; ColombiaFil: Eiglsperger, Johannes. Numares GmbH; AlemaniaFil: Piraux, Bernard. Université Catholique de Louvain; BélgicaAmerican Physical Society2014-02-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/94789Frapiccini, Ana Laura; Hamido, Aliou; Schröter, Sebastian; Pyke, Dean; Mota Furtado, Francisca; et al.; Explicit schemes for time propagating many-body wave functions; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 89; 2; 14-2-2014; 1-151050-29471094-1622CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.023418info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.89.023418info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1401.6318info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:41:19Zoai:ri.conicet.gov.ar:11336/94789instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:41:19.456CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Explicit schemes for time propagating many-body wave functions
title Explicit schemes for time propagating many-body wave functions
spellingShingle Explicit schemes for time propagating many-body wave functions
Frapiccini, Ana Laura
TDSE
Explicit propagator
Arnoldi
Runge-Kutta
title_short Explicit schemes for time propagating many-body wave functions
title_full Explicit schemes for time propagating many-body wave functions
title_fullStr Explicit schemes for time propagating many-body wave functions
title_full_unstemmed Explicit schemes for time propagating many-body wave functions
title_sort Explicit schemes for time propagating many-body wave functions
dc.creator.none.fl_str_mv Frapiccini, Ana Laura
Hamido, Aliou
Schröter, Sebastian
Pyke, Dean
Mota Furtado, Francisca
O’Mahony, Patrick F.
Madroñero, Javier
Eiglsperger, Johannes
Piraux, Bernard
author Frapiccini, Ana Laura
author_facet Frapiccini, Ana Laura
Hamido, Aliou
Schröter, Sebastian
Pyke, Dean
Mota Furtado, Francisca
O’Mahony, Patrick F.
Madroñero, Javier
Eiglsperger, Johannes
Piraux, Bernard
author_role author
author2 Hamido, Aliou
Schröter, Sebastian
Pyke, Dean
Mota Furtado, Francisca
O’Mahony, Patrick F.
Madroñero, Javier
Eiglsperger, Johannes
Piraux, Bernard
author2_role author
author
author
author
author
author
author
author
dc.subject.none.fl_str_mv TDSE
Explicit propagator
Arnoldi
Runge-Kutta
topic TDSE
Explicit propagator
Arnoldi
Runge-Kutta
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrödinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.
Fil: Frapiccini, Ana Laura. Université Catholique de Louvain; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Fil: Hamido, Aliou. Université Catholique de Louvain; Bélgica
Fil: Schröter, Sebastian. Technische Universitat München; Alemania
Fil: Pyke, Dean. University of London; Reino Unido
Fil: Mota-Furtado, Francisca. University of London; Reino Unido
Fil: O’Mahony, Patrick F.. University of London; Reino Unido
Fil: Madroñero, Javier. Universidad del Valle; Colombia
Fil: Eiglsperger, Johannes. Numares GmbH; Alemania
Fil: Piraux, Bernard. Université Catholique de Louvain; Bélgica
description Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrödinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.
publishDate 2014
dc.date.none.fl_str_mv 2014-02-14
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/94789
Frapiccini, Ana Laura; Hamido, Aliou; Schröter, Sebastian; Pyke, Dean; Mota Furtado, Francisca; et al.; Explicit schemes for time propagating many-body wave functions; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 89; 2; 14-2-2014; 1-15
1050-2947
1094-1622
CONICET Digital
CONICET
url http://hdl.handle.net/11336/94789
identifier_str_mv Frapiccini, Ana Laura; Hamido, Aliou; Schröter, Sebastian; Pyke, Dean; Mota Furtado, Francisca; et al.; Explicit schemes for time propagating many-body wave functions; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 89; 2; 14-2-2014; 1-15
1050-2947
1094-1622
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.023418
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.89.023418
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1401.6318
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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