Numerical methods for computing Casimir interactions

Abstract

We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria---choice of problem, basis, and solution technique---that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.

46 pages, 142 references, 5 figures. To appear in upcoming Lecture Notes in Physics book on Casimir Physics

References in corpus (15)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Casimir forces in a T operator approach
• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Worldline algorithms for Casimir configurations
• 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
• Roughness correction to the Casimir force : Beyond the Proximity Force Approximation
• Casimir Forces in a Piston Geometry at Zero and Finite Temperatures
• Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• Achieving a Strongly Temperature-Dependent Casimir Effect
• Microstructure Effects for Casimir Forces in Chiral Metamaterials
• Casimir energy and geometry : beyond the Proximity Force Approximation

Cited by in corpus (149)

• A Materials Perspective on Casimir and van der Waals Interactions
• Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects
• Non-equilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force
• Quantum control and long-range quantum correlations in dynamical Casimir arrays
• Lateral Casimir force on a rotating particle near a planar surface
• Nonclassical microwave radiation from the dynamical Casimir effect
• Casimir Force Phase Transitions in the Graphene Family
• Amplified opto-mechanical transduction of virtual radiation pressure
• The Reality of Casimir Friction
• A Scattering Approach to the Dynamical Casimir Effect
• Ultrasensitive Inertial and Force Sensors with Diamagnetically Levitated Magnets
• 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
• Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings
• Strong thermal and electrostatic manipulation of the Casimir force in graphene multilayers
• Quantum friction between graphene sheets
• The Casimir-Polder effect for a stack of conductive planes
• Frequency-dependent dielectric function of semiconductors with application to physisorption
• Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall
• Casimir force between Weyl semimetals in a chiral medium
• Electromagnetic description of three-dimensional time-reversal invariant ponderable topological insulators
• Nonequilibrium Tuning of the Thermal Casimir Effect
• Casimir interaction between a sphere and a grating
• Approximate analytical results on the cavity dynamical Casimir effect in the presence of a two-level atom
• Fluctuation-Induced Phenomena in Nanoscale Systems: Harnessing the Power of Noise
• Wading through the void: Exploring quantum friction and nonequilibrium fluctuations
• Microscopic dynamical Casimir effect
• A simple model for the dynamical Casimir effect for a static mirror with time-dependent properties
• Casimir switch: steering optical transparency with vacuum forces
• Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum
• Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges
• Topological quantum friction
• Theory of optomechanics: Oscillator-field model of moving mirrors
• Functional approach to quantum friction: effective action and dissipative force
• Nonperturbative Casimir effect and monopoles: compact Abelian gauge theory in two spatial dimensions
• Detecting the Curvature of de Sitter Universe with Two Entangled Atoms
• Dynamical Casimir Effect in cavity with N-level detector or N-1 two-level atoms
• Enhanced resonant force between two entangled identical atoms in a photonic crystal
• Effective Landau-Zener transitions in circuit dynamical Casimir effect with time-varying modulation frequency
• Vacuum fluctuations and generalized boundary conditions
• The Casimir effect and deconfinement phase transition
• Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
• Cavity Dynamical Casimir Effect in the presence of a three-level atom
• Quantum Corrections to Soliton Energies
• Electromagnetic Waves in a Model with Chern-Simons Potential
• Molecular recognition by van der Waals interaction between polymers with sequence-specific polarizabilities
• Tidal and nonequilibrium Casimir effects in free fall
• Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium
• Vacuum currents in braneworlds on AdS bulk with compact dimensions
• van der Waals Interaction Energy Between Two Atoms Moving With Uniform Acceleration
• Casimir forces in inhomogeneous media: renormalization and the principle of virtual work
• Surface Vacuum Energy in Cutoff Models: Pressure Anomaly and Distributional Gravitational Limit
• Motion induced radiation and quantum friction for a moving atom
• Quantum dissipative effects in moving imperfect mirrors: sidewise and normal motions
• Inhibition of the dynamical Casimir effect with Robin boundary conditions
• Quantum work distributions associated with the dynamical Casimir effect
• Thermal corrections to quantum friction and decoherence: a Closed-Time-Path approach to atom-surface interaction
• Casimir effect for scalar current densities in topologically nontrivial spaces
• Casimir Self-Entropy of a Spherical Electromagnetic $\delta$-Function Shell
• Control of the Radiative Heat Transfer in a Pair of Rotating Nanostructures
• Quantum Vacuum Sagnac Effect
• Dynamical Casimir effect with $\delta -{\delta }^{\prime }$ mirrors
• Superconducting circuit boundary conditions beyond the Dynamical Casimir Effect
• Casimir effect from a scattering approach
• Dark Matter Axions, Non-Newtonian Gravity and Constraints on them from Recent Measurement of the Casimir Force in the Micrometer Separation Range
• Dynamical Casimir effect in nonlinear vibrating cavities
• Macroscopic Quantum Electrodynamics and Density Functional Theory Approaches to Dispersion Interactions between Fullerenes
• Vacuum energy density and pressure near a soft wall
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Casimir boundaries, monopoles, and deconfinement transition in 3+1 dimensional compact electrodynamics
• Dynamical Casimir effect for semitransparent mirrors
• Strong coupling of Rydberg atoms and surface phonon polaritons on piezoelectric superlattices
• Fluctuation-induced Interactions in Micro- and Nano-systems: Survey of Some Basic Results
• Local Casimir Effect for a Scalar Field in Presence of a Point Impurity
• Renormalization for a Scalar Field in an External Scalar Potential
• Electromagnetic Casimir effect for conducting plates in de Sitter spacetime
• Born-series approach to the calculation of Casimir forces
• Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption
• Analytical comparison of the first- and second-order resonances for implementation of the dynamical Casimir effect in nonstationary circuit QED
• Non-trivial retardation effects in dispersion forces: From anomalous distance dependence to novel traps
• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Light-induced optomechanical forces in graphene waveguides
• Casimir Effect : Theory and Experiments
• Unifying Theory for Casimir Forces: Bulk and Surface Formulations
• Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Time-dependent Robin boundary conditions in the dynamical Casimir effect
• Premelting and formation of ice due to Casimir-Lifshitz interactions: Impact of improved parameterization for materials
• Casimir-Polder Interaction of an Atom with a Cavity Wall Made of Phase-Change Material out of Thermal Equilibrium
• The cutoff-dependence of the Casimir force within an inhomogeneous medium
• Influence of the field-detector coupling strength on the dynamical Casimir effect
• Anti-Dynamical Casimir Effect as a Resource for Work Extraction
• Numerical approach to simulating interference phenomena in a two-oscillating mirrors cavity
• Entanglement degradation of cavity modes due to the dynamical Casimir effect
• Wightman function and the Casimir effect for a Robin sphere in a constant curvature space
• Nano-scale thermal transfer -- an invitation to fluctuation electrodynamics
• Lorentz violating scalar Casimir effect for a $D$-dimensional sphere
• Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case
• Hydrodynamic fluctuation-induced forces in confined fluids
• Einstein-Rosen bridge from the minimal length
• Fluctuation-induced forces between rings threaded around a polymer chain under tension
• Dynamical Casimir effect via four- and five-photon transitions using a strongly detuned atom
• The Casimir densities for a sphere in the Milne universe
• On non-equilibrium photon distributions in the Casimir effect
• Damped vacuum states of light
• Remarks on distinguishability of Schwarzschild spacetime and thermal Minkowski spacetime using Resonance Casimir-Polder interaction
• Quantum vacuum effects in braneworlds on AdS bulk
• Phonon-photon conversion as mechanism for cooling and coherence transfer
• Dynamical Casimir effect via modulated Kerr or higher nonlinearities
• Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities
• Quantum Brownian motion for a particle in analog expanding cosmologies in the presence of disclination
• Casimir Energy Corrections by Light-Cone Fluctuations
• Thermal radiation forces on planar structures with asymmetric optical response
• Four-Fermion Interaction Model on ${\mathcal{M}}^{D-1}\otimes S^1$
• Examining a covariant and renormalizable quantum field theory in de Sitter space by studying "black hole radiation"
• Casimir forces and quantum friction of finite-size atoms in relativistic trajectories
• Explosive particle creation by instantaneous change of boundary condition
• Casimir effect for fermion condensate in conical rings
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Electromagnetic Casimir densities for a cylindrical shell on de Sitter space
• Casimir energy due to inhomogeneous thin plates
• Electromagnetic field quantization in the presence of a rotating body
• Motion induced excitation and radiation from an atom facing a mirror
• How the mass of a scalar field influences Resonance Casimir-Polder interaction in Schwarzschild spacetime
• Dynamical Casimir-Polder potentials in non-adiabatic conditions
• Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field
• Casimir Energy in (2 + 1)-Dimensional Field Theories
• Vacuum polarization with zero-range potentials on a hyperplane
• Foundational Issues in Dynamical Casimir Effect and Analogue Features in Cosmological Particle Creation
• Van der Waals interaction between polymers with sequence-specific polarizabilities: Stiff polymers and flexible Gaussian coils
• Phonon Pumping by Modulating the Ultrastrong Vacuum
• Casimir-Lifshitz force for graphene-covered gratings
• Thermal Radiation Force and Torque on Moving Nanostructures with Anisotropic Optical Response
• Anisotropic resonance energy transfer with strained phosphorene
• Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry
• How to strengthen constraints on non-Newtonian gravity from measuring the lateral Casimir force
• Quantum effects due to a moving Dirichlet point
• Motion induced excitation and electromagnetic radiation from an atom facing a thin mirror
• Atom-Field-Medium Interactions I: Graded Influence Actions for $N$ Harmonic Atoms in a Dielectric-Altered Quantum Field
• Interplay of curvature and temperature in the Casimir-Polder interaction
• Thermodynamic perspective on quantum fluctuations
• Quantum dissipative effects in graphene-like mirrors
• Vacuum currents in elliptic pseudosphere tubes
• Tailoring the van der Waals interaction with rotation
• Casimir effect with dielectric matter in salted water and implications at the cell scale
• From Brownian motion formalism to fluctuation-induced force in a general fluctuating medium
• Shortcuts to adiabaticity, unexciting backgrounds, and reflectionless potentials
• Modified discrete Laguerre polynomials for efficient computation of exponentially bounded Matsubara sums
• Corrected Proximity-Force Approximation for Lateral Casimir Forces