Spectrum and normal modes of non-Hermitian quadratic boson operators

Autores
Garcia, Javier; Rossignoli, Raúl Dante
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We analyze the spectrum and normal-mode representation of general quadratic bosonic forms H not necessarily Hermitian. It is shown that, in the one-dimensional case, such forms exhibit either a harmonic regime where both H and H† have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where either H or H† have a continuous complex twofold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Nondiagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension to N-dimensional quadratic systems is also discussed.
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina
Materia
Boson
Nonhermitian
Quadratic forms
Eigenstates
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/50051
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/50051
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Spectrum and normal modes of non-Hermitian quadratic boson operatorsGarcia, JavierRossignoli, Raúl DanteBosonNonhermitianQuadratic formsEigenstateshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We analyze the spectrum and normal-mode representation of general quadratic bosonic forms H not necessarily Hermitian. It is shown that, in the one-dimensional case, such forms exhibit either a harmonic regime where both H and H† have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where either H or H† have a continuous complex twofold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Nondiagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension to N-dimensional quadratic systems is also discussed.Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; ArgentinaAmerican Physical Society2017-12info: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/11336/50051Garcia, Javier; Rossignoli, Raúl Dante; Spectrum and normal modes of non-Hermitian quadratic boson operators; American Physical Society; Physical Review A; 96; 6; 12-2017; 621300-6213102469-9926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.96.062130info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.062130info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:34:35Zoai:ri.conicet.gov.ar:11336/50051instacron: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 10:34:35.319CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spectrum and normal modes of non-Hermitian quadratic boson operators
title Spectrum and normal modes of non-Hermitian quadratic boson operators
spellingShingle Spectrum and normal modes of non-Hermitian quadratic boson operators
Garcia, Javier
Boson
Nonhermitian
Quadratic forms
Eigenstates
title_short Spectrum and normal modes of non-Hermitian quadratic boson operators
title_full Spectrum and normal modes of non-Hermitian quadratic boson operators
title_fullStr Spectrum and normal modes of non-Hermitian quadratic boson operators
title_full_unstemmed Spectrum and normal modes of non-Hermitian quadratic boson operators
title_sort Spectrum and normal modes of non-Hermitian quadratic boson operators
dc.creator.none.fl_str_mv Garcia, Javier
Rossignoli, Raúl Dante
author Garcia, Javier
author_facet Garcia, Javier
Rossignoli, Raúl Dante
author_role author
author2 Rossignoli, Raúl Dante
author2_role author
dc.subject.none.fl_str_mv Boson
Nonhermitian
Quadratic forms
Eigenstates
topic Boson
Nonhermitian
Quadratic forms
Eigenstates
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 analyze the spectrum and normal-mode representation of general quadratic bosonic forms H not necessarily Hermitian. It is shown that, in the one-dimensional case, such forms exhibit either a harmonic regime where both H and H† have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where either H or H† have a continuous complex twofold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Nondiagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension to N-dimensional quadratic systems is also discussed.
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina
description We analyze the spectrum and normal-mode representation of general quadratic bosonic forms H not necessarily Hermitian. It is shown that, in the one-dimensional case, such forms exhibit either a harmonic regime where both H and H† have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where either H or H† have a continuous complex twofold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Nondiagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension to N-dimensional quadratic systems is also discussed.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
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/11336/50051
Garcia, Javier; Rossignoli, Raúl Dante; Spectrum and normal modes of non-Hermitian quadratic boson operators; American Physical Society; Physical Review A; 96; 6; 12-2017; 621300-621310
2469-9926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/50051
identifier_str_mv Garcia, Javier; Rossignoli, Raúl Dante; Spectrum and normal modes of non-Hermitian quadratic boson operators; American Physical Society; Physical Review A; 96; 6; 12-2017; 621300-621310
2469-9926
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.96.062130
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.062130
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/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
_version_ 1844614363374157824
score 13.070432

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