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  • 1.
    Bordag, Michael
    et al.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Nikolaev, Vladimir
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    First analytic correction beyond the proximity force approximation in the Casimir effect for the electromagnetic field in sphere-plane geometry2010In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 81, no 6, p. Article number 065011-Article in journal (Refereed)
    Abstract [en]

    We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio epsilon. This correction is of order epsilon. Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, epsilon ln epsilon and epsilon(ln epsilon)(2). We compare this result with the available findings of numerical and experimental approaches.

  • 2.
    Teo, L. P.
    et al.
    Univ Nottingham Malaysia Campus, Fac Engn, Dept Appl Math, Semenyih 43500, Selangor Darul, Malaysia .
    Bordag, M.
    Univ Leipzig, D-04103 Leipzig, Germany .
    Nikolaev, V.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Corrections beyond the proximity force approximation2011In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 84, no 12, p. 125037-Article in journal (Refereed)
    Abstract [en]

    We recalculate the first analytic correction beyond proximity force approximation for a sphere in front of a plane for a scalar field and for the electromagnetic field. We use the method of Bordag and Nikolaev [J. Phys. A 41, 164002 (2008)]. We confirm their result for Dirichlet boundary conditions whereas we find a different one for Robin, Neumann and conductor boundary conditions. The difference can be traced back to a sign error. As a result, the corrections depend on the Robin parameter. Agreement is found with a very recent method of derivative expansion.

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