Scattering Theory Approach to Electrodynamic Casimir Forces

Abstract

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

43 pages, 10 figures

References in corpus (19)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Measurement of the Casimir force between a gold sphere and silicon surface with nanoscale trench arrays
• Control of the Casimir force by the modification of dielectric properties with light
• Casimir forces in a T operator approach
• The Casimir force and the quantum theory of lossy optical cavities
• Casimir Forces between Compact Objects: I. The Scalar Case
• Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry
• Demonstration of the difference Casimir force for samples with different charge carrier densities
• Exact Casimir interaction between eccentric cylinders
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Precision measurement of the Casimir-Lifshitz force in a fluid
• Casimir interaction between plane and spherical metallic surfaces
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• Transition from Casimir to van der Waals force between macroscopic bodies
• Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
• Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders
• The Casimir effect as scattering problem

Cited by in corpus (235)

• A Materials Perspective on Casimir and van der Waals Interactions
• Numerical methods for computing Casimir interactions
• Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects
• Non-equilibrium electromagnetic fluctuations: Heat transfer and interactions
• Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies
• Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate
• Casimir forces on a silicon micromechanical chip
• Casimir forces beyond the proximity approximation
• Fluctuating surface-current formulation of radiative heat transfer: theory and applications
• Investigation of the Casimir interaction between two magnetic metals in comparison with nonmagnetic test bodies
• Exact microscopic theory of electromagnetic heat transfer between a dielectric sphere and plate
• Casimir-Lifshitz force out of thermal equilibrium and heat transfer between arbitrary bodies
• Material dependence of Casimir forces: gradient expansion beyond proximity
• Measurement of the gradient of the Casimir force between a nonmagnetic sphere and a magnetic plate
• Non-equilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force
• Constraints on stable equilibria with fluctuation-induced forces
• Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: incandecence and luminescence in arbitrary geometries
• Heat radiation from long cylindrical objects
• Repulsive Casimir Effect with Chern insulators
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• Non-touching nanoparticle diclusters bound by repulsive and attractive Casimir forces
• Chiral Casimir Forces: Repulsive, Enhanced, Tunable
• Thermal Casimir effect for Drude metals in the plane-sphere geometry
• Radiative heat transfer and nonequilibrium Casimir-Lifshitz force in many-body systems with planar geometry
• The Casimir force on a surface with shallow nanoscale corrugations: Geometry and finite conductivity effects
• A Minimal Nuclear Energy Density Functional
• Probing the Casimir force with optical tweezers
• Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory
• Modeling near-field radiative heat transfer from sharp objects using a general 3d numerical scattering technique
• Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation
• Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids
• Many body heat radiation and heat transfer in the presence of a non-absorbing background medium
• A Scattering Approach to the Dynamical Casimir Effect
• Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution
• Casimir force between sharp-shaped conductors
• Spontaneous emission by rotating objects: A scattering approach
• Classical and fluctuation-induced electromagnetic interactions in micronscale systems: designer bonding, antibonding, and Casimir forces
• Fluctuation-induced forces between inclusions in a fluid membrane under tension
• Heat radiation and transfer for point particles in arbitrary geometries
• Modal Approach to Casimir Forces in Periodic Structures
• Fluctuating Surface Currents: A New Algorithm for Efficient Prediction of Casimir Interactions among Arbitrary Materials in Arbitrary Geometries. I. Theory
• Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models
• Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings
• Casimir-Polder effect for a plane with Chern-Simons interaction
• Casimir-Polder interaction between an atom and a dielectric grating
• Magnetic materials and the problem of thermal Casimir force
• Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry
• Hide it to see it better: a robust setup to probe the thermal Casimir effect
• Material dependence of Casimir interaction between a sphere and a plate: First analytic correction beyond proximity force approximation
• Heat radiation and transfer in confinement
• Nonequilibrium Atom-Dielectric Forces Mediated by a Quantum Field
• Casimir interaction between a cylinder and a plate at finite temperature: Exact results and comparison to proximity force approximation
• Electromagnetic description of three-dimensional time-reversal invariant ponderable topological insulators
• Experimental and theoretical investigation of the thermal effect in the Casimir interaction from graphene
• Microstructure Effects for Casimir Forces in Chiral Metamaterials
• Casimir Force at a Knife's Edge
• Casimir interaction between a sphere and a grating
• Computation of Casimir Interactions between Arbitrary 3D Objects with Arbitrary Material Properties
• Casimir effect between two spheres at small separations
• Fluctuation-Induced Phenomena in Nanoscale Systems: Harnessing the Power of Noise
• First analytic correction to the proximity force approximation in the Casimir effect between two parallel cylinders
• Unifying microscopic and continuum treatments of van der Waals and Casimir interactions
• The Casimir effect: medium and geometry
• Casimir Energy and Entropy in the Sphere--Sphere Geometry
• Proximity force approximation and specular reflection: Application of the WKB limit of Mie scattering to the Casimir effect
• An alternative response to the off-shell quantum fluctuations: A step forward in resolution of the Casimir puzzle
• Tunable Casimir equilibria with phase change materials: from quantum trapping to its release
• Fermionic Casimir effect in a field theory model with Lorentz symmetry violation
• Fundamental limits to attractive and repulsive Casimir--Polder forces
• Linear response relations in fluctuational electrodynamics
• The Casimir effect as a sum-over-modes in dissipative systems
• Casimir densities for a spherical boundary in de Sitter spacetime
• Fluctuational electrodynamics of hyperbolic metamaterials
• A diagrammatic expansion of the Casimir energy in multiple reflections: theory and applications
• Conformal Field Theory of Critical Casimir Interactions in 2D
• Casimir spring and compass: Stable levitation and alignment of compact objects
• Universality versus material dependence of fluctuation forces between metallic wires
• Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics
• Constraints on axion-nucleon coupling constants from measuring the Casimir force between corrugated surfaces
• Scattering theory without large-distance asymptotics
• Lifshitz theory of van der Waals pressure in dissipative media
• Casimir entropy for magnetodielectrics
• Casimir repulsion between Topological Insulators in the diluted regime
• Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion
• Probing the screening of the Casimir interaction with optical tweezers
• Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches
• The Casimir pressure between metallic plates out of thermal equilibrium: Proposed test for the relaxation properties of free electrons
• Scattering theory of the screened Casimir interaction in electrolytes
• Scattering theory without large-distance asymptotics in arbitrary dimensions
• Casimir interactions of an object inside a spherical metal shell
• A quasi-analytical modal approach for computing Casimir interactions in periodic nanostructures
• Observing the Casimir-Lifshitz Force Out of Thermal Equilibrium
• Edges and Diffractive Effects in Casimir Energies
• Casimir energy between media-separated cylinders: the scalar case
• Mode summation approach to Casimir effect between two objects
• Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response
• Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries
• Anisotropic particles near surfaces: Self-propulsion and friction
• Multiple scattering expansion for dielectric media: Casimir effect
• Multiple Scattering Casimir Force Calculations: Layered and Corrugated Materials, Wedges, and Casimir-Polder Forces
• Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics
• Beyond-PFA Casimir Force between two spheres at finite temperature
• How to confirm and exclude different models of material properties in the Casimir effect
• Heat-kernel approach for scattering
• Trace Expressions and Associated Limits for Non-Equilibrium Casimir Torque
• Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals
• Scattering Approach for Fluctuation--Induced Interactions at Fluid Interfaces
• Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium
• Casimir potential of a compact object enclosed by a spherical cavity
• Disorder in quantum vacuum: Casimir-induced localization of matter waves
• Fluctuational electrodynamics for nonlinear media
• Microscopic theory of photon-induced energy, momentum, and angular momentum transport in the nonequilibrium regime
• Phonon-polariton mediated thermal radiation and heat transfer among molecules and macroscopic bodies: nonlocal electromagnetic response at mesoscopic scales
• Casimir repulsive-attractive transition between liquid-separated dielectric metamaterial and metal
• Structural anisotropy and orientation-induced Casimir repulsion in fluids
• Casimir interaction of two dielectric half spaces with Chern-Simons boundary layers
• Casimir entropy and nonlocal response functions to the off-shell quantum fluctuations
• Quantum field theory of the Casimir force for graphene
• Beyond-proximity-force-approximation Casimir force between two spheres at finite temperature II: plasma versus Drude modeling, grounded versus isolated spheres
• Fluctuation-induced Interactions in Micro- and Nano-systems: Survey of Some Basic Results
• Equilibrium forces on non-reciprocal materials
• Casimir energies in spherically symmetric background potentials revisited
• Casimir interaction between inclined metallic cylinders
• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Born-series approach to the calculation of Casimir forces
• Layer Response Theory: Energetics of layered materials from semi-analytic high-level theory
• Nuclear Energy Density Functionals: What do we really know?
• Variable Phase S-Matrix Calculations for Asymmetric Potentials and Dielectrics
• Thermal Casimir Force between Magnetic Materials
• Unifying Theory for Casimir Forces: Bulk and Surface Formulations
• Inhomogeneity-Induced Casimir Transport of Nanoparticles
• Quantum propulsion and trapping of nano-objects by inhomogeneity-induced lateral Casimir forces
• Experimentum crucis for electromagnetic response of metals to evanescent waves and the Casimir puzzle
• Casimir and Casimir-Polder forces with dissipation from first principles
• Topologically protected Casimir effect for lattice fermions
• Geometry and material effects in Casimir physics - Scattering theory
• The Casimir effect in graphene systems: Experiment and theory
• Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force
• Casimir Energies of Periodic Dielectric Gratings
• Electromagnetic Casimir Forces in Elliptic Cylinder Geometries
• Edge Corrections to Electromagnetic Casimir Energies From General-Purpose Mathieu Function Routines
• Classical Casimir interaction of perfectly conducting sphere and plate
• The Casimir effect for fields with arbitrary spin
• Scalar Casimir effect between two concentric spheres
• Inhomogeneity-related cutoff dependence of the Casimir energy and stress
• Vacuum local and global electromagnetic self-energies for a point-like and an extended field source
• Attractive Electromagnetic Casimir Stress on a Spherical Dielectric Shell
• Casimir effect in the scattering approach: correlations between material properties, temperature and geometry
• Sphere-plate Casimir interaction in (D+1)-dimensional spacetime
• Regularization versus renormalization: Why are Casimir energy differences so often finite?
• Casimir Physics: Geometry, Shape and Material
• High-accuracy Casimir-Polder force calculations using the Discontinuous Galerkin Time-Domain method
• Universal Casimir attraction between filaments at the cell scale
• Casimir micro-sphere diclusters and three-body effects in fluids
• Electromagnetic Casimir Energies of Semi-Infinite Planes
• A mathematical analysis of Casimir interactions I: The scalar field
• Three Body Fluctuation-Induced Interaction at Fluid Interfaces: A Strong Deviation from the Pairwise Summation
• Casimir interaction between a sphere and a cylinder
• Effect of Curvature and Confinement on the Casimir-Polder Interaction
• Accounting for dissipation in the scattering approach to the Casimir energy
• Heat radiation and transfer for nanoparticles in the presence of a cylinder
• On the Sign of Fermion-Mediated Interactions
• First-order correction to the Casimir force within an inhomogeneous medium
• The Casimir Effect in Spheroidal Geometries
• Casimir self-stress in a dielectric sphere
• Exact classical sphere-plate Casimir interaction in (D+1)-dimensional spacetime
• The Casimir force, causality and the Gurzhi model
• Casimir Energy and Entropy between perfect metal Spheres
• Calculation of nonzero-temperature Casimir forces in the time domain
• Casimir repulsion turned into attraction by the nonlocal response of salted water
• Ab-initio theory of quantum fluctuations and relaxation oscillations in multimode lasers
• Ferminoic Casimir effect between spheres
• Membrane-mediated interactions
• Casimir forces and quantum friction of finite-size atoms in relativistic trajectories
• Casimir interaction between spheres in $(\mathbf{D}+1)$-dimensional Minkowski spacetime
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Casimir interaction of arbitrarily shaped conductors
• Attractive and repulsive fluctuation-induced pressure in peptide films deposited on semiconductor substrates
• Material Dependence of the Wire-Particle Casimir Interaction
• Stochastic Quantization and Casimir Forces
• Worldline approach for numerical computation of electromagnetic Casimir energies. I. Scalar field coupled to magnetodielectric media
• Casimir self-energy of a δ-δ' sphere
• Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
• Implications of the Babinet Principle for Casimir Interactions
• Finite temperature Casimir interaction between spheres in $(D+1)$-dimensional spacetime: Exact computations and asymptotic expansions
• Repulsive Casimir-Lifshitz pressure in closed cavities
• Phonon Casimir effect in polyatomic systems
• Electromagnetic Casimir-Polder Interaction for a Conducting Cone
• Twist-induced near-field radiative thermal regulator assisted by cylindrical surface modes
• Casimir interaction of concentric spheres at finite temperature
• Casimir-Polder interaction with Chern-Simons boundary layers
• How to strengthen constraints on non-Newtonian gravity from measuring the lateral Casimir force
• Renyi information from entropic effects in one higher dimension
• Statistical approach to Casimir-Polder potentials in heterogeneous media
• Fluctuational Electrodynamics in Atomic and Macroscopic Systems: van der Waals Interactions and Radiative Heat Transfer
• On the Difference Between the Vacuum Casimir Energies for Grounded and Isolated Conductors
• On the Casimir repulsion in sphere-plate geometry
• Calculating Casimir interactions for Periodic Surface Relief Gratings using the C-Method
• Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
• A robust superconducting setup to probe the thermal Casimir effect
• Casimir interaction between spherical and planar plasma sheets
• Exact Electromagnetic Casimir Energy of a Disk Opposite a Plane
• Zero and finite temperature Casimir effect of massive vector field between real metals
• Casimir Forces in Multi-Sphere Configurations
• Casimir torque between two inhomogeneous semi-transparent concentric cylinders
• Normal and lateral Casimir force: Advances and prospects
• Probability Thermodynamics and Probability Quantum Field
• Time-dependent radiative heat flux after the beginning of thermal radiation
• Fluctuations of the energy density and intensity for arbitrary objects in an arbitrary environment
• Casimir energy of smooth compact surfaces
• A generalized bag-like boundary condition for fields with arbitrary spin
• Scalar Casimir effect between two concentric D-dimensional spheres
• Propulsion force and heat transfer for nonreciprocal nanoparticles
• Scattering approach for calculating one-loop effective action and vacuum energy
• Casimir forces from a loop integral formulation
• On the Casimir Energy of Frequency Dependent Interactions
• Lateral Casimir force between deeply corrugated dielectric and metallic plates
• Vacuum energy of scalar fields on spherical shells with general matching conditions
• Scattering theory without large-distance asymptotics: scattering boundary condition
• Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip
• Corrected Proximity-Force Approximation for Lateral Casimir Forces
• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory
• Casimir effect in twisted photonic gratings with in-plane chirality
• Fractal Interpretation of Bacterial Light Harvesters
• Casimir Interaction between Polydisperse Colloids Trapped at a Fluid Interface
• Surface alignment disorder and pseudo-Casimir forces in smectic-A liquid crystalline films
• Searching Repulsive Casimir Forces Between Magneto-Electric Materials
• Casimir forces between spheres
• Renormalization for singular-potential scattering
• 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
• Universal Theory of Light Scattering of Randomly Oriented Particles: A Fluctuational-Electrodynamics Approach for Modeling of Light Transport in Disordered Nanostructures
• Casimir-Lifshitz pressure on cavity walls
• Casimir entropy and internal energy of the objects in fluctuating scalar and electromagnetic fields
• Radiative heat transfer with a cylindrical waveguide decays logarithmically slow