Material dependence of Casimir forces: Gradient expansion beyond proximity

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51 , 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quan...

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Bibliographic Details
Published in:Applied physics letters 2012-02, Vol.100 (7), p.074110-074110-4
Main Authors: Bimonte, Giuseppe, Emig, Thorsten, Kardar, Mehran
Format: Article
Language:English
Subjects:
Condensed Matter
Physics
Quantum Physics
Statistical Mechanics
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Summary:A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51 , 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here, we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) at room temperature. We derive an explicit expression for the amplitude θ ̂ 1 of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, θ ̂ 1 has an unusually large temperature dependence.
ISSN:0003-6951
1077-3118
DOI:10.1063/1.3686903