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Towards the Calculation of Casimir Forces for Inhomogeneous Planar Media

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Computer Mathematics
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Abstract

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.

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Acknowledgments

The authors are supported by EPSRC grant EP/CS23229/1. UL is also supported by a Royal Society Wolfson Research Merit Award. We would like to acknowledge the critical discussions we have had with Tom Philbin.

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Correspondence to T. W. Kelsey .

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Xiong, C., Kelsey, T.W., Linton, S.A., Leonhardt, U. (2014). Towards the Calculation of Casimir Forces for Inhomogeneous Planar Media. In: Feng, R., Lee, Ws., Sato, Y. (eds) Computer Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43799-5_15

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