Proximity force approximation for the Casimir energy as a derivative expansion

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 part...

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Autores principales:	Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D.
Formato:	JOUR
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_15507998_v84_n10_p_Fosco
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_15507998_v84_n10_p_Fosco2023-10-03T16:24:28Z Proximity force approximation for the Casimir energy as a derivative expansion Fosco, C.D. Lombardo, F.C. Mazzitelli, F.D. 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:Lombardo, F.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Mazzitelli, F.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15507998_v84_n10_p_Fosco
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
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.
format	JOUR
author	Fosco, C.D. Lombardo, F.C. Mazzitelli, F.D.
spellingShingle	Fosco, C.D. Lombardo, F.C. Mazzitelli, F.D. Proximity force approximation for the Casimir energy as a derivative expansion
author_facet	Fosco, C.D. Lombardo, F.C. Mazzitelli, F.D.
author_sort	Fosco, C.D.
title	Proximity force approximation for the Casimir energy as a derivative expansion
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
url	http://hdl.handle.net/20.500.12110/paper_15507998_v84_n10_p_Fosco
work_keys_str_mv	AT foscocd proximityforceapproximationforthecasimirenergyasaderivativeexpansion AT lombardofc proximityforceapproximationforthecasimirenergyasaderivativeexpansion AT mazzitellifd proximityforceapproximationforthecasimirenergyasaderivativeexpansion
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Proximity force approximation for the Casimir energy as a derivative expansion

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