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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/94789
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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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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