Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions

We apply the derivative expansion approach to the Casimir effect for a real scalar field in d spatial dimensions to calculate the next-to-leading-order term in that expansion, namely, the first correction to the proximity force approximation. The field satisfies either Dirichlet or Neumann boundary...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Lombardo, Fernando César, Mazzitelli, Francisco Diego
Publicado: 2012
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15507998_v86_n4_p_Fosco
http://hdl.handle.net/20.500.12110/paper_15507998_v86_n4_p_Fosco
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15507998_v86_n4_p_Fosco
record_format dspace
spelling paper:paper_15507998_v86_n4_p_Fosco2023-06-08T16:22:32Z Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions Lombardo, Fernando César Mazzitelli, Francisco Diego We apply the derivative expansion approach to the Casimir effect for a real scalar field in d spatial dimensions to calculate the next-to-leading-order term in that expansion, namely, the first correction to the proximity force approximation. The field satisfies either Dirichlet or Neumann boundary conditions on two static mirrors, one of them flat and the other gently curved. We show that, for Dirichlet boundary conditions, the next-to-leading-order term in the Casimir energy is of quadratic order in derivatives, regardless of the number of dimensions. Therefore, it is local and determined by a single coefficient. We show that the same holds true, if d*2, for a field which satisfies Neumann conditions. When d=2, the next-to-leading-order term becomes nonlocal in coordinate space, a manifestation of the existence of a gapless excitation (which does exist also for d>2, but produces subleading terms). We also consider a derivative expansion approach including thermal fluctuations of the scalar field. We show that, for Dirichlet mirrors, the next-to-leading- order term in the free energy is also local for any temperature T. Besides, it interpolates between the proper limits: when T→0, it tends to the one we had calculated for the Casimir energy in d dimensions, while for T→∞, it corresponds to the one for a theory in d-1 dimensions, because of the expected dimensional reduction at high temperatures. For Neumann mirrors in d=3, we find a nonlocal next-to-leading-order term for any T>0. © 2012 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15507998_v86_n4_p_Fosco http://hdl.handle.net/20.500.12110/paper_15507998_v86_n4_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 We apply the derivative expansion approach to the Casimir effect for a real scalar field in d spatial dimensions to calculate the next-to-leading-order term in that expansion, namely, the first correction to the proximity force approximation. The field satisfies either Dirichlet or Neumann boundary conditions on two static mirrors, one of them flat and the other gently curved. We show that, for Dirichlet boundary conditions, the next-to-leading-order term in the Casimir energy is of quadratic order in derivatives, regardless of the number of dimensions. Therefore, it is local and determined by a single coefficient. We show that the same holds true, if d*2, for a field which satisfies Neumann conditions. When d=2, the next-to-leading-order term becomes nonlocal in coordinate space, a manifestation of the existence of a gapless excitation (which does exist also for d>2, but produces subleading terms). We also consider a derivative expansion approach including thermal fluctuations of the scalar field. We show that, for Dirichlet mirrors, the next-to-leading- order term in the free energy is also local for any temperature T. Besides, it interpolates between the proper limits: when T→0, it tends to the one we had calculated for the Casimir energy in d dimensions, while for T→∞, it corresponds to the one for a theory in d-1 dimensions, because of the expected dimensional reduction at high temperatures. For Neumann mirrors in d=3, we find a nonlocal next-to-leading-order term for any T>0. © 2012 American Physical Society.
author Lombardo, Fernando César
Mazzitelli, Francisco Diego
spellingShingle Lombardo, Fernando César
Mazzitelli, Francisco Diego
Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions
author_facet Lombardo, Fernando César
Mazzitelli, Francisco Diego
author_sort Lombardo, Fernando César
title Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions
title_short Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions
title_full Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions
title_fullStr Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions
title_full_unstemmed Derivative expansion for the Casimir effect at zero and finite temperature in d+1 dimensions
title_sort derivative expansion for the casimir effect at zero and finite temperature in d+1 dimensions
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15507998_v86_n4_p_Fosco
http://hdl.handle.net/20.500.12110/paper_15507998_v86_n4_p_Fosco
work_keys_str_mv AT lombardofernandocesar derivativeexpansionforthecasimireffectatzeroandfinitetemperatureind1dimensions
AT mazzitellifranciscodiego derivativeexpansionforthecasimireffectatzeroandfinitetemperatureind1dimensions
_version_ 1768543484408496128

Ejemplares similares