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Towards the calculation of Casimir forces for inhomogeneous planar media

Research output: Chapter in Book/Report/Conference proceedingChapter


Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations toward the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green’s functions is at the boundatry 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 indicate the possibility of alternative regularizations. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and suggest combined numerical and symbolic approaches toward a more general computational framework.


Original languageEnglish
Title of host publicationComputer Mathematics
Subtitle of host publication9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012, Contributed Papers and Invited Talks
EditorsRuyong Feng, Wen-shin Lee, Yosuke Sato
ISBN (Electronic)978-3-662-43799-5
ISBN (Print)978-3-662-43798-8
Publication statusPublished - 1 Oct 2014

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