Exact zero-point interaction energy between cylinders

Abstract

We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding to this configuration are studied both analytically and numerically. These include concentric cylinders, cylinder-plane, and eccentric cylinders, for small and large separations between the surfaces. For small separations we recover the proximity approximation, while for large separations we find a weak logarithmic decay of the Casimir interaction energy, typical of cylindrical geometries.

20 pages, 7 figures

References in corpus (6)

• Casimir interaction between a plate and a cylinder
• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Casimir effect for curved geometries: PFA validity limits
• Lateral Casimir force beyond the Proximity Force Approximation
• Exact Casimir interaction between eccentric cylinders
• The Casimir force between rough metallic plates

Cited by in corpus (43)

• A Materials Perspective on Casimir and van der Waals Interactions
• Casimir forces between arbitrary compact objects
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Multiple Scattering Methods in Casimir Calculations
• Thermal Casimir effect for Drude metals in the plane-sphere geometry
• Exploring the quantum vacuum with cylinders
• Recent Developments in the Casimir Effect
• Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
• Casimir interaction between a cylinder and a plate at finite temperature: Exact results and comparison to proximity force approximation
• Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
• Casimir effect between two spheres at small separations
• First analytic correction to the proximity force approximation in the Casimir effect between two parallel cylinders
• The Casimir effect as scattering problem
• Interplay between geometry and temperature for inclined Casimir plates
• Lateral Casimir-Polder force with corrugated surfaces
• Universality versus material dependence of fluctuation forces between metallic wires
• Numerical evaluation of the Casimir interaction between cylinders
• Scalar Casimir-Polder forces for uniaxial corrugations
• Geothermal Casimir phenomena for the sphere-plate and cylinder-plate configurations
• Mode summation approach to Casimir effect between two objects
• Casimir energy between media-separated cylinders: the scalar case
• Casimir energy and geometry : beyond the Proximity Force Approximation
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals
• Geothermal Casimir Phenomena
• Landauer's formula breakdown for radiative heat transfer and non-equilibrium Casimir forces
• Casimir effect in the scattering approach: correlations between material properties, temperature and geometry
• Casimir interaction between a sphere and a cylinder
• The Dirichlet Casimir Energy For ϕ^4 Theory in a Rectangular Waveguide
• Novel Casimir wormholes in Einstein gravity
• Ferminoic Casimir effect between spheres
• Computing the Casimir energy using the point-matching method
• Casimir interaction between spheres in $(\mathbf{D}+1)$-dimensional Minkowski spacetime
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Finite temperature Casimir interaction between spheres in $(D+1)$-dimensional spacetime: Exact computations and asymptotic expansions
• On the accuracy of the PFA: analogies between Casimir and electrostatic forces
• Casimir-Lifshitz interaction between ZnO and SiO2 nanorods in bromobenzene: retardation effects turn the interaction repulsive at intermediate separations
• Casimir interaction of concentric spheres at finite temperature
• Casimir interaction between spherical and planar plasma sheets
• Casimir torque between two inhomogeneous semi-transparent concentric cylinders
• Casimir interaction between two concentric cylinders at nonzero temperature
• The proximity force approximation for the Casimir energy of plate-sphere and sphere-sphere systems in the presence of one extra compactified universal dimension
• Massive scalar Casimir interaction beyond proximity force approximation