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

• URL: http://arxiv.org/abs/2103.13927v1
• Date: Thu, 25 Mar 2021 15:39:50 GMT
• Title: Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
• Authors: Vinicius Henning, Benjamin Spreng, Paulo A. Maia Neto, Gert-Ludwig Ingold
• Abstract summary: We consider the Casimir interaction energy between a plane and a sphere of radius $R$ at finite temperature $T$. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\lambda_T=\hbar c/k_\mathrm{B}T$ 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.

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