Conical Casimir Pistons with Hybrid Boundary Conditions

Abstract

In this paper we compute the Casimir energy and force for massless scalar fields endowed with hybrid boundary conditions, in the setting of the bounded generalized cone. By using spectral zeta function regularization methods, we obtain explicit expressions for the Casimir energy and force in arbitrary dimensions in terms of the zeta function defined on the piston. Our general formulas are, subsequently, specialized to the case in which the piston is modelled by a $d$-dimensional sphere. In this particular situation, explicit results are given for $d=2,3,4,5$.

LaTex, 26 Pages

References in corpus (11)

• Casimir force on a piston
• Casimir interaction of two plates inside a cylinder
• Casimir piston for massless scalar fields in three dimensions
• Casimir Forces in a Piston Geometry at Zero and Finite Temperatures
• Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs
• Casimir pistons with hybrid boundary conditions
• Kaluza-Klein models as pistons
• Iterated amplitudes in the high-energy limit
• The Casimir Effect for Conical Pistons
• Zeta Determinant for Laplace Operators on Riemann Caps
• Spherical Casimir pistons

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• Casimir-Polder interaction between an atom and a conducting wall in cosmic string spacetime
• Casimir Pistons with General Boundary Conditions
• The Casimir Effect for Generalized Piston Geometries
• The Casimir effect for pistons with transmittal boundary conditions
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Casimir interaction of concentric spheres at finite temperature
• Scalar Casimir effect between two concentric D-dimensional spheres