Casimir Energies of Cylinders: Universal Function

Abstract

New exact results are given for the interior Casimir energies of infinitely long waveguides of triangular cross section (equilateral, hemiequilateral, and isosceles right triangles). Results for cylinders of rectangular cross section are rederived. In particular, results are obtained for interior modes belonging to Dirichlet and Neumann boundary conditions (TM and TE modes). These results are expressed in rapidly convergent series using the Chowla-Selberg formula, and in fact may be given in closed form, except for general rectangles. The energies are finite because only the first three heat-kernel coefficients can be nonzero for the case of polygonal boundaries. What appears to be a universal behavior of the Casimir energy as a function of the shape of the regular or quasi-regular cross-sectional figure is presented. Furthermore, numerical calculations for arbitrary right triangular cross sections suggest that the universal behavior may be extended to waveguides of general polygonal cross sections. The new exact and numerical results are compared with the proximity force approximation (PFA).

29 pages, 9 figures

References in corpus (12)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Precise comparison of theory and new experiment for the Casimir force leads to stronger constraints on thermal quantum effects and long-range interactions
• How Does Casimir Energy Fall?
• Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
• Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
• Energy of the vacuum with a perfectly conducting and infinite cylindrical surface
• Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs
• Repulsive Casimir Pistons
• The heat kernel expansion for the electromagnetic field in a cavity
• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Local and Global Casimir Energies for a Semitransparent Cylindrical Shell
• Casimir energy inside a triangle

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