Born-series approach to the calculation of Casimir forces

Bennett, R. (2014) Born-series approach to the calculation of Casimir forces. Physical Review A: Atomic, Molecular and Optical Physics, 89(6), 062512. (doi: 10.1103/PhysRevA.89.062512)

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The Casimir force between two objects is notoriously difficult to calculate in anything other than parallel-plate geometries due to its nonadditive nature. This means that for more complicated, realistic geometries one usually has to resort to approaches such as making the crude proximity force approximation (PFA). Another issue with calculation of Casimir forces in real-world situations (such as with realistic materials) is that there are continuing doubts about the status of Lifshitz's original treatment as a true quantum theory. Here we demonstrate an alternative approach to the calculation of Casimir forces for arbitrary geometries which sidesteps both of these problems. Our calculations are based upon a Born expansion of the Green's function of the quantized electromagnetic vacuum field, interpreted as multiple scattering, with the relevant coupling strength being the difference in the dielectric functions of the various materials involved. This allows one to consider arbitrary geometries in single or multiple scattering simply by integrating over the desired shape, meaning that extension beyond the PFA is trivial. This work is mostly dedicated to illustration of the method by reproduction of known parallel-slab results—a process that turns out to be nontrivial and provides several useful insights. We also present a short example of calculation of the Casimir energy for a more complicated geometry; namely, that of two finite slabs.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bennett, Dr Robert
Authors: Bennett, R.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Physical Review A: Atomic, Molecular and Optical Physics
Publisher:American Physical Society
ISSN (Online):1094-1622
Published Online:30 June 2014

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