Unifying Theory for Casimir Forces: Bulk and Surface Formulations

Abstract

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

arXiv comment37 pages, 2 figures

References in corpus (28)

• The Casimir force between real materials: experiment and theory
• A Materials Perspective on Casimir and van der Waals Interactions
• Casimir forces between arbitrary compact objects
• Scattering Theory Approach to Electrodynamic Casimir Forces
• Opposites Attract - A Theorem About The Casimir Force
• Numerical methods for computing Casimir interactions
• Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects
• 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
• Normal and Lateral Casimir Forces between Deformed Plates
• Casimir Forces between Compact Objects: I. The Scalar Case
• A scattering approach to Casimir forces and radiative heat transfer for nanostructured surfaces out of thermal equilibrium
• Efficient Computation of Casimir Interactions between Arbitrary 3D Objects
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Non-equilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force
• Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation
• Towards a Theory of Molecular Forces between Deformed Media
• Classical and fluctuation-induced electromagnetic interactions in micronscale systems: designer bonding, antibonding, and Casimir forces
• Fluctuating Surface Currents: A New Algorithm for Efficient Prediction of Casimir Interactions among Arbitrary Materials in Arbitrary Geometries. I. Theory
• Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
• Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry
• Material dependence of Casimir interaction between a sphere and a plate: First analytic correction beyond proximity force approximation
• Shape-dependence of near-field heat transfer between a spheroidal nanoparticle and a flat surface
• Heat transfer between anisotropic nanopartricles: Enhancement and switching
• Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries
• Beyond-proximity-force-approximation Casimir force between two spheres at finite temperature II: plasma versus Drude modeling, grounded versus isolated spheres
• Non-superposition effects in the Dirichlet Casimir effect
• Exact Electromagnetic Casimir Energy of a Disk Opposite a Plane

Cited by in corpus (6)

• Multiple scattering expansion for dielectric media: Casimir effect
• Scalar-Mediated Quantum Forces Between Macroscopic Bodies and Interferometry
• Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force
• Casimir Forces in CFT with Defects and Boundaries
• Electromagnetic Casimir-Polder Interaction for a Conducting Cone
• The relative trace formula in electromagnetic scattering and boundary layer operators