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

• Autores: Fosco, Cesar Daniel; Lombardo, Fernando Cesar; Mazzitelli, Francisco Diego
• Año de publicación: 2012
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Casimir; Proximity; Temperature; Approximation
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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: Fosco, Cesar Daniel. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
Fil: Lombardo, Fernando Cesar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física. Grupo de Física Teórica; 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física. Grupo de Física Teórica; 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