Non-contact gears: II. Casimir torque between concentric corrugated cylinders for the scalar case

Abstract

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for non-contact gears. To this end, we calculate the Casimir torque between two such cylinders, described by $\delta$-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed.

9 pages, 3 figures, references corrected

References in corpus (5)

• Casimir Forces between Compact Objects: I. The Scalar Case
• Non-contact rack and pinion powered by the lateral Casimir force
• Multiple Scattering Methods in Casimir Calculations
• Exploring the quantum vacuum with cylinders
• Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates

Cited by in corpus (8)

• Recent Developments in the Casimir Effect
• Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
• Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates
• Scalar Casimir-Polder forces for uniaxial corrugations
• Electromagnetic $\delta$-function sphere
• Irreducible Many-Body Casimir Energies of Intersecting Objects
• Leading- and next-to-leading-order lateral Casimir force on corrugated surfaces
• On the Casimir interaction between two smoothly deformed cylindrical surfaces