Proximity force approximation for the Casimir energy as a derivative expansion

Autores
Fosco, Cesar Daniel; Lombardo, Fernando Cesar; Mazzitelli, Francisco Diego
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next-to-leading-order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function ψ in front of a plane. By regarding the Casimir energy as a functional of ψ, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of the corresponding NTLO correction, which involves two derivatives of ψ. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy. © 2011 American Physical Society.
Fil: Fosco, Cesar Daniel. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Nacional de Cuyo; Argentina
Fil: Lombardo, Fernando Cesar. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Mazzitelli, Francisco Diego. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Materia
Efecto Casimir
Derivative Expansion
Effective Action
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:11336/56646
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/56646
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Proximity force approximation for the Casimir energy as a derivative expansionFosco, Cesar DanielLombardo, Fernando CesarMazzitelli, Francisco DiegoEfecto CasimirDerivative ExpansionEffective Actionhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next-to-leading-order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function ψ in front of a plane. By regarding the Casimir energy as a functional of ψ, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of the corresponding NTLO correction, which involves two derivatives of ψ. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy. © 2011 American Physical Society.Fil: Fosco, Cesar Daniel. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Lombardo, Fernando Cesar. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Mazzitelli, Francisco Diego. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaAmerican Physical Society2011-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/56646Fosco, Cesar Daniel; Lombardo, Fernando Cesar; Mazzitelli, Francisco Diego; Proximity force approximation for the Casimir energy as a derivative expansion; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 84; 10; 11-2011; 1050311-10503161550-7998CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.84.105031info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:29:10Zoai:ri.conicet.gov.ar:11336/56646instacron: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:34982025-10-22 11:29:11.003CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Proximity force approximation for the Casimir energy as a derivative expansion
title Proximity force approximation for the Casimir energy as a derivative expansion
spellingShingle Proximity force approximation for the Casimir energy as a derivative expansion
Fosco, Cesar Daniel
Efecto Casimir
Derivative Expansion
Effective Action
title_short Proximity force approximation for the Casimir energy as a derivative expansion
title_full Proximity force approximation for the Casimir energy as a derivative expansion
title_fullStr Proximity force approximation for the Casimir energy as a derivative expansion
title_full_unstemmed Proximity force approximation for the Casimir energy as a derivative expansion
title_sort Proximity force approximation for the Casimir energy as a derivative expansion
dc.creator.none.fl_str_mv Fosco, Cesar Daniel
Lombardo, Fernando Cesar
Mazzitelli, Francisco Diego
author Fosco, Cesar Daniel
author_facet Fosco, Cesar Daniel
Lombardo, Fernando Cesar
Mazzitelli, Francisco Diego
author_role author
author2 Lombardo, Fernando Cesar
Mazzitelli, Francisco Diego
author2_role author
author
dc.subject.none.fl_str_mv Efecto Casimir
Derivative Expansion
Effective Action
topic Efecto Casimir
Derivative Expansion
Effective Action
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next-to-leading-order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function ψ in front of a plane. By regarding the Casimir energy as a functional of ψ, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of the corresponding NTLO correction, which involves two derivatives of ψ. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy. © 2011 American Physical Society.
Fil: Fosco, Cesar Daniel. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Nacional de Cuyo; Argentina
Fil: Lombardo, Fernando Cesar. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Mazzitelli, Francisco Diego. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
description The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next-to-leading-order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function ψ in front of a plane. By regarding the Casimir energy as a functional of ψ, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of the corresponding NTLO correction, which involves two derivatives of ψ. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy. © 2011 American Physical Society.
publishDate 2011
dc.date.none.fl_str_mv 2011-11
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/11336/56646
Fosco, Cesar Daniel; Lombardo, Fernando Cesar; Mazzitelli, Francisco Diego; Proximity force approximation for the Casimir energy as a derivative expansion; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 84; 10; 11-2011; 1050311-1050316
1550-7998
CONICET Digital
CONICET
url http://hdl.handle.net/11336/56646
identifier_str_mv Fosco, Cesar Daniel; Lombardo, Fernando Cesar; Mazzitelli, Francisco Diego; Proximity force approximation for the Casimir energy as a derivative expansion; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 84; 10; 11-2011; 1050311-1050316
1550-7998
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/PhysRevD.84.105031
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
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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score 13.238319

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