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Towards the Calculation of Casimir Forces for Inhomogeneous Planar Media

In: Computer Mathematics

Author

Listed:
  • C. Xiong

    (University of St Andrews, School of Computer Science)

  • T. W. Kelsey

    (University of St Andrews, School of Computer Science)

  • S. A. Linton

    (University of St Andrews, School of Computer Science)

  • U. Leonhardt

    (University of St Andrews, School of Physics and Astronomy)

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.

Suggested Citation

  • C. Xiong & T. W. Kelsey & S. A. Linton & U. Leonhardt, 2014. "Towards the Calculation of Casimir Forces for Inhomogeneous Planar Media," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 171-180, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_15
    DOI: 10.1007/978-3-662-43799-5_15
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