Is space-time symmetry a suitable generalization of parity-time symmetry?

Autores
Amore, Paolo; Fernández, Francisco Marcelo; Garcia, Javier
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We discuss space-time symmetric Hamiltonian operators of the form H = H0 + igH ′ , where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g < gc , where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.
Fil: Amore, Paolo. Universidad de Colima; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Materia
Pt-Symmetry
Space-Time Symmetry
Non-Hermitian Hamiltonian
Multidimensional System
Nivel de accesibilidad
acceso embargado
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/5157
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Is space-time symmetry a suitable generalization of parity-time symmetry?Amore, PaoloFernández, Francisco MarceloGarcia, JavierPt-SymmetrySpace-Time SymmetryNon-Hermitian HamiltonianMultidimensional Systemhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We discuss space-time symmetric Hamiltonian operators of the form H = H0 + igH ′ , where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g < gc , where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.Fil: Amore, Paolo. Universidad de Colima; MéxicoFil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; ArgentinaElsevier2014-08-08info:eu-repo/date/embargoEnd/2016-09-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/5157Amore, Paolo ; Fernández, Francisco Marcelo; Garcia, Javier; Is space-time symmetry a suitable generalization of parity-time symmetry?; Elsevier; Annals Of Physics (new York); 350; 8-8-2014; 533-5480003-4916enginfo:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.5234info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S000349161400205Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2014.07.026info:eu-repo/semantics/embargoedAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:49:56Zoai:ri.conicet.gov.ar:11336/5157instacron: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:34982025-11-12 09:49:56.829CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Is space-time symmetry a suitable generalization of parity-time symmetry?
title Is space-time symmetry a suitable generalization of parity-time symmetry?
spellingShingle Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo
Pt-Symmetry
Space-Time Symmetry
Non-Hermitian Hamiltonian
Multidimensional System
title_short Is space-time symmetry a suitable generalization of parity-time symmetry?
title_full Is space-time symmetry a suitable generalization of parity-time symmetry?
title_fullStr Is space-time symmetry a suitable generalization of parity-time symmetry?
title_full_unstemmed Is space-time symmetry a suitable generalization of parity-time symmetry?
title_sort Is space-time symmetry a suitable generalization of parity-time symmetry?
dc.creator.none.fl_str_mv Amore, Paolo
Fernández, Francisco Marcelo
Garcia, Javier
author Amore, Paolo
author_facet Amore, Paolo
Fernández, Francisco Marcelo
Garcia, Javier
author_role author
author2 Fernández, Francisco Marcelo
Garcia, Javier
author2_role author
author
dc.subject.none.fl_str_mv Pt-Symmetry
Space-Time Symmetry
Non-Hermitian Hamiltonian
Multidimensional System
topic Pt-Symmetry
Space-Time Symmetry
Non-Hermitian Hamiltonian
Multidimensional System
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We discuss space-time symmetric Hamiltonian operators of the form H = H0 + igH ′ , where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g < gc , where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.
Fil: Amore, Paolo. Universidad de Colima; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
description We discuss space-time symmetric Hamiltonian operators of the form H = H0 + igH ′ , where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g < gc , where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.
publishDate 2014
dc.date.none.fl_str_mv 2014-08-08
info:eu-repo/date/embargoEnd/2016-09-08
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/11336/5157
Amore, Paolo ; Fernández, Francisco Marcelo; Garcia, Javier; Is space-time symmetry a suitable generalization of parity-time symmetry?; Elsevier; Annals Of Physics (new York); 350; 8-8-2014; 533-548
0003-4916
url http://hdl.handle.net/11336/5157
identifier_str_mv Amore, Paolo ; Fernández, Francisco Marcelo; Garcia, Javier; Is space-time symmetry a suitable generalization of parity-time symmetry?; Elsevier; Annals Of Physics (new York); 350; 8-8-2014; 533-548
0003-4916
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.5234
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S000349161400205X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2014.07.026
dc.rights.none.fl_str_mv info:eu-repo/semantics/embargoedAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv embargoedAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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score 12.976206

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