Casimir forces for inhomogeneous planar media
MetadataShow full item record
Casimir forces arise from vacuum uctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases condence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specic calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.
Xiong , C , Kelsey , T , Linton , S A & Leonhardt , U 2013 , Casimir forces for inhomogeneous planar media . in Journal of Physics: Conference Series . 1 edn , vol. 401 , Journal of Physics: Conference Series , no. 1 , vol. 410 . https://doi.org/10.1088/1742-6596/410/1/012165
Journal of Physics: Conference Series
© 2013 Xiong et al. This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 3.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.