Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures

Abstract

We consider the Casimir interaction energy between a plane and a sphere of radius $R$ at finite temperature $T$ as a function of the distance of closest approach $L$. Typical experimental conditions are such that the thermal wavelength ${\lambda }_T=\hslash c/k_{\mathrm{B}}T$ satisfies the condition $L\ll {\lambda }_T\ll R$. We derive the leading correction to the proximity-force approximation valid for such intermediate temperatures by developing the scattering formula in the plane-wave basis. Our analytical result captures the joint effect of the spherical geometry and temperature and is written as a sum of temperature-dependent logarithmic terms. Surprisingly, two of the logarithmic terms arise from the Matsubara zero-frequency contribution.

arXiv comment20 pages, 3 figures

References in corpus (49)

• The Casimir force between real materials: experiment and theory
• Casimir forces between arbitrary compact objects
• Observation of the thermal Casimir force
• Scattering Theory Approach to Electrodynamic Casimir Forces
• The Casimir effect within scattering theory
• Temperature dependence of the Casimir effect between metallic mirrors
• Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies
• Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using atomic force microscope in a frequency shift technique
• The Casimir force and the quantum theory of lossy optical cavities
• Isoelectronic determination of the thermal Casimir force
• Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate
• Casimir forces beyond the proximity approximation
• The proximity force approximation for the Casimir energy as a derivative expansion
• Casimir force between partially transmitting mirrors
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Casimir Force and In Situ Surface Potential Measurements on Nanomembranes
• Thermal Casimir Effect in the Plane-Sphere Geometry
• Thermal Casimir effect for Drude metals in the plane-sphere geometry
• Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory
• Probing the Casimir force with optical tweezers
• Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation
• Precision measurements of the gradient of the Casimir force between ultra clean metallic surfaces at larger separations
• Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models
• Examining the Casimir puzzle with upgraded technique and advanced surface cleaning
• Vacuum energy between a sphere and a plane at finite temperature
• Quantum dissipative Brownian motion and the Casimir effect
• On the corrections beyond proximity force approximation (PFA)
• Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry
• First analytic correction beyond PFA for the electromagnetic field in sphere-plane geometry
• Non-monotonic thermal Casimir force from geometry-temperature interplay
• 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
• Classical Casimir interaction in the plane-sphere geometry
• The derivative expansion approach to the interaction between close surfaces
• Geothermal Casimir phenomena for the sphere-plate and cylinder-plate configurations
• Derivative expansion for the Casimir effect at zero and finite temperature in $d+1$ dimensions
• Measurement of the Casimir force in a gas and in a liquid
• The role of diffraction in the Casimir effect beyond the proximity force approximation
• Plane-wave approach to the exact van der Waals interaction between colloid particles
• Recent measurements of the Casimir force: Comparison between experiment and theory
• Advancing numerics for the Casimir effect to experimentally relevant aspect ratios
• Disentangling geometric and dissipative origins of negative Casimir entropies
• Progress in Experimental Measurements of the Surface-Surface Casimir Force: Electrostatic Calibrations and Limitations to Accuracy
• Beyond-proximity-force-approximation Casimir force between two spheres at finite temperature II: plasma versus Drude modeling, grounded versus isolated spheres
• Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach
• Classical Casimir interaction of perfectly conducting sphere and plate
• On the Derivative Expansion for the Electromagnetic Casimir Free Energy at High Temperatures
• Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures

Cited by in corpus (2)

• Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
• Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves