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  • 1.
    Bordag, Michael
    et al.
    Univ Leipzig, Vor Hospitaltore 1, D-04103 Leipzig, Germany..
    Nikolaev, Vladimir
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).
    Analytic corrections to the electromagnetic casimir interaction between a sphere and a plate at shortdistances2010In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 25, no 11, p. 2171-2176Article in journal (Refereed)
    Abstract [en]

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

  • 2.
    Bordag, Michael
    et al.
    Leipzig University, Vor Dem Hospitaltore 1, D-04103 Leipzig, Germany.
    Nikolaev, Vladimir
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Analytic corrections to the electromagnetic casimir interaction between a sphere and a plate at shortdistances2010In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 25, no 11, p. 2171-2176Article in journal (Refereed)
    Abstract [en]

    For the vacuum interaction of asphere in front of a plane,both obeying conductor boundary conditions, we consider the approximation of small separation. We derive the next-to-leading order of the asymptotic expansion in the separation-to-radius ratio epsilon. This correction is of order epsilon. In 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.

  • 3.
    Bordag, Michael
    et al.
    Leipzig University, Vor dem Hospitaltore 1, D-04103 Leipzig, Germany.
    Nikolaev, Vladimir
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Beyond proximity force approximation in the casimir effect2009In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 24, no 8-9, p. 1743-1747Article in journal (Refereed)
    Abstract [en]

    We compare the analytical and numerical results for the Casimir force for the configuration of a plane and a cylinder in front of a plane. While for Dirichlet boundary conditions on both, plane and sphere or cylinder, agreement is found, for Neumann boundary conditions on either the plane or one of the two, cylinder or sphere, disagreement is found. This holds, for a sphere, also for different boundary conditions on the interacting surfaces. From recent, new numerical results for the cylinder, a general appearance of logarithmic contributions beyond PFA can be predicted.

  • 4.
    Bordag, Michael
    et al.
    Institute for Theoretical Physics, Leipzig University, Leipzig, Germany.
    Nikolaev, Vladimir
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Casimir force for a sphere in front of a plane beyond proximity force approximation2008In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 41, no 16, p. 164002-Article in journal (Refereed)
    Abstract [en]

    For the configuration of a sphere in front of a plane, we calculate the first two terms of the asymptotic expansion for small separation of the Casimir force. We consider both Dirichlet and Neumann boundary conditions.

  • 5.
    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.

  • 6.
    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).
    The vacuum energy for two cylinders with one increasing in size2009In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 42, no 41, p. 415203-Article in journal (Refereed)
    Abstract [en]

    We consider the vacuum energy for the configuration of two cylinders and obtain its asymptotic expansion if the radius of one of these cylinders becomes large while the radius of the other one and their separation are kept fixed. We calculate explicitly the next-to-leading order correction to the vacuum energy for the radius of the other cylinder becoming large or small.

  • 7.
    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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