Edges and Diffractive Effects in Casimir Energies
arXiv:1002.3575 · doi:10.1103/PhysRevD.81.125013
Abstract
The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single plate with a slit in it, perpendicular plates separated by a gap, and two parallel plates, one of which has a long slit of large width, related to the case of one plate being semi-infinite. We develop a general formalism for studying such problems, based on the wavefunctional for the field in the gap between the plates. This formalism leads to a lower dimensional theory defined on the open regions of the plates or boundaries. The Casimir energy is then given in terms of the determinant of the nonlocal differential operator which defines the lower dimensional theory. We develop perturbative methods for computing these determinants. Our results are in good agreement with known results based on Monte Carlo simulations. The method is well suited to isolating the diffractive contributions to the Casimir energy.
32 pages, LaTeX, 9 figures. v2: additional discussion of renormalization procedure, version to appear in PRD. v3: corrected a sign error in (70)
References in corpus (14)
- Casimir forces between arbitrary compact objects
- Scattering Theory Approach to Electrodynamic Casimir Forces
- Casimir forces in a T operator approach
- Casimir Forces between Compact Objects: I. The Scalar Case
- Casimir edge effects
- Multiple Scattering Methods in Casimir Calculations
- Recent Developments in the Casimir Effect
- Casimir Force at a Knife's Edge
- Interplay between geometry and temperature for inclined Casimir plates
- Multiple Scattering Casimir Force Calculations: Layered and Corrugated Materials, Wedges, and Casimir-Polder Forces
- Geothermal Casimir Phenomena
- Geometry-Temperature Interplay in the Casimir Effect
- Weak Coupling Casimir Energies for Finite Plate Configurations
- From multiple scattering to van der Waals interactions: exact results for eccentric cylinders
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