Casimir force between sharp-shaped conductors

Abstract

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.

References in corpus (31)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Measurement of the Casimir force between parallel metallic surfaces
• Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates
• Casimir forces between arbitrary compact objects
• Scattering Theory Approach to Electrodynamic Casimir Forces
• Opposites Attract - A Theorem About The Casimir Force
• Casimir interaction between a plate and a cylinder
• Measurement of the Casimir force between a gold sphere and silicon surface with nanoscale trench arrays
• Casimir forces in a T operator approach
• Quantum levitation by left-handed metamaterials
• Worldline algorithms for Casimir configurations
• Efficient Computation of Casimir Interactions between Arbitrary 3D Objects
• Casimir edge effects
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Casimir forces between cylinders and plates
• Thermal Casimir Effect in the Plane-Sphere Geometry
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• Bohr-van Leeuwen theorem and the thermal Casimir effect for conductors
• The Casimir force at high temperature
• Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models
• Casimir force between two ideal-conductor walls revisited
• Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders
• Interplay between geometry and temperature for inclined Casimir plates
• Edges and Diffractive Effects in Casimir Energies
• Possibility to measure thermal effects in the Casimir force
• Fluctuation-induced interactions between dielectrics in general geometries
• Geothermal Casimir Phenomena
• Casimir effect at nonzero temperature for wedges and cylinders
• Geometry-Temperature Interplay in the Casimir Effect
• Ingredients of a Casimir analog computer

Cited by in corpus (38)

• A Materials Perspective on Casimir and van der Waals Interactions
• A Scattering Approach to the Dynamical Casimir Effect
• Classical and fluctuation-induced electromagnetic interactions in micronscale systems: designer bonding, antibonding, and Casimir forces
• Fluctuation-Induced Phenomena in Nanoscale Systems: Harnessing the Power of Noise
• Polymer-mediated entropic forces between scale-free objects
• Entropic force of polymers on a cone tip
• Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries
• Many-Body Contributions to Green's Functions and Casimir Energies
• Multiple scattering expansion for dielectric media: Casimir effect
• Interplay of roughness/modulation and curvature at proximity
• Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals
• Scattering Approach for Fluctuation--Induced Interactions at Fluid Interfaces
• Casimir Energy for a Coupled Fermion-Kink System and its stability
• Impact of nuclear vibrations on van der Waals and Casimir interactions at zero and finite temperature
• Electromagnetic Casimir Forces in Elliptic Cylinder Geometries
• Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force
• Edge Corrections to Electromagnetic Casimir Energies From General-Purpose Mathieu Function Routines
• Vacuum local and global electromagnetic self-energies for a point-like and an extended field source
• An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition
• Electromagnetic Casimir Energies of Semi-Infinite Planes
• High-accuracy Casimir-Polder force calculations using the Discontinuous Galerkin Time-Domain method
• Diffractive Effects and General Boundary Conditions in Casimir Energy
• Effect of Curvature and Confinement on the Casimir-Polder Interaction
• Quantum particle in a spherical well confined by a cone
• Thermal diffractive corrections to Casimir energies
• Material Dependence of the Wire-Particle Casimir Interaction
• Stochastic Quantization and Casimir Forces
• Fluctuational Electrodynamics in Atomic and Macroscopic Systems: van der Waals Interactions and Radiative Heat Transfer
• Electromagnetic Casimir-Polder Interaction for a Conducting Cone
• Quantum Energy Density of Cosmic Strings with Nonzero Radius
• Exact Electromagnetic Casimir Energy of a Disk Opposite a Plane
• Casimir effect: Edges and diffraction
• Reversing the Critical Casimir force by shape deformation
• Stochastic Quantization and Casimir Forces: Pistons of Arbitrary Cross Section
• Complex orientation dependence of Casimir-Polder interaction induced by curvature and optical properties of the surface and the surrounding medium
• Casimir torque in weak coupling
• On the Shape Dependence of the Tangential Casimir Force
• Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension