Casimir Interaction between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
We consider the Casimir interaction energy between a plane and a sphere of radius <i>R</i> at finite temperature <i>T</i> as a function of the distance of closest approach <i>L</i>. Typical experimental conditions are such that the thermal wavelength <inline-fo...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-05-01
|
| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/7/5/129 |
| Summary: | We consider the Casimir interaction energy between a plane and a sphere of radius <i>R</i> at finite temperature <i>T</i> as a function of the distance of closest approach <i>L</i>. Typical experimental conditions are such that the thermal wavelength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>λ</mi><mi>T</mi></msub><mo>=</mo><mi>ℏ</mi><mi>c</mi><mo>/</mo><msub><mi>k</mi><mi mathvariant="normal">B</mi></msub><mi>T</mi></mrow></semantics></math></inline-formula> satisfies the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>≪</mo><msub><mi>λ</mi><mi>T</mi></msub><mo>≪</mo><mi>R</mi></mrow></semantics></math></inline-formula>. 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. |
|---|---|
| ISSN: | 2218-1997 |