Volume 118, Number 2, April 2017
|Number of page(s)||7|
|Published online||20 June 2017|
Going beyond PFA: A precise formula for the sphere-plate Casimir force
Dipartimento di Fisica E. Pancini, Università di Napoli Federico II, Complesso Universitario MSA Via Cintia, I-80126 Napoli, Italy and INFN, Sezione di Napoli - I-80126 Napoli, Italy
Received: 23 May 2017
Accepted: 7 June 2017
Quantum fluctuations of the electromagnetic field in the medium surrounding two discharged macroscopic polarizable bodies induce a force between the two bodies, the so-called Casimir force. In the last two decades many experiments have accurately measured this force, and significant efforts are made to harness it in the actuation of micro- and nano-machines. The inherent many-body character of the Casimir force makes its computation very difficult in non-planar geometries, like the standard experimental sphere-plate configuration. Here we derive an approximate semi-analytic formula for the sphere-plate Casimir force, which is both easy to compute numerically and very accurate at all distances. By a comparison with the fully converged exact scattering formula, we show that the error made by the approximate formula is indeed much smaller than the uncertainty of present and foreseeable Casimir experiments.
PACS: 03.70.+k – Theory of quantized fields / 12.20.-m – Quantum electrodynamics / 42.25.Fx – Diffraction and scattering
© EPLA, 2017
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