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Volumn 58, Issue 2, 1998, Pages 935-953

Infinity-free semiclassical evaluation of Casimir effects

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EID: 4143143892     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.935     Document Type: Article
Times cited : (108)

References (36)
  • 1
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    • SPHJAR
    • Casimir effects involving dielectrics were first studied by E.M. Lifshitz, Zh. Éksp. Teor. Fiz. 29, 94 (1955) [Sov. Phys. JETP 2, 73 (1956)], and might well be referred to as Casimir-Lifshitz, effects. SPHJAR
    • (1956) Sov. Phys. JETP , vol.2 , pp. 73
    • Lifshitz, E.M.1
  • 3
    • 0001748257 scopus 로고
    • PYLAAG
    • The generalized argument theorem, first introduced in this area by N.G. van Kampen, B.R.A. Nijboer, and K. Schramm, Phys. Lett. 26A, 307 (1968), greatly simplifies the discussion. See also Ref. 2 for a nice review of the material.PYLAAG
    • (1968) Phys. Lett. , vol.26A , pp. 307
    • van Kampen, N.G.1    Nijboer, B.R.A.2    Schramm, K.3
  • 4
  • 8
  • 12
    • 0039266262 scopus 로고
    • PHYSAG
    • M.J. Sparnaay, Physica 24, 751 (1958); PHYSAG
    • (1958) Physica , vol.24 , pp. 751
    • Sparnaay, M.J.1
  • 18
    • 0040130720 scopus 로고
    • B.R. Levy and J.B. Keller, Can. J. Phys. 38, 128 (1960); CJPHADW. Franz, Theorie der Beugung Elektromagnetischer Wellen (Springer, Berlin 1957);
    • (1960) Can. J. Phys. , vol.38 , pp. 128
    • Levy, B.R.1    Keller, J.B.2
  • 19
  • 23
    • 0011217067 scopus 로고
    • PLRAAN See also L. Spruch, in Long-Range Casimir Forces: Theory and Experiment in Multiparticle Dynamics, edited by F.S. Levin and D.A. Micha (Plenum, New York, 1993), Chap. 1
    • L. Spruch, J.F. Babb, and F. Zhou, Phys. Rev. A 49, 2476 (1994). PLRAANSee also L. Spruch, in Long-Range Casimir Forces: Theory and Experiment in Multiparticle Dynamics, edited by F.S. Levin and D.A. Micha (Plenum, New York, 1993), Chap. 1.
    • (1994) Phys. Rev. A , vol.49 , pp. 2476
    • Spruch, L.1    Babb, J.F.2    Zhou, F.3
  • 24
    • 0004254722 scopus 로고
    • Springer, New York
    • See, for example, L.E. Reichl, The Transition to Chaos (Springer, New York, 1992), Chap. 8 and references therein.
    • (1992) The Transition to Chaos
    • Reichl, L.E.1
  • 25
    • 85037225266 scopus 로고    scopus 로고
    • The semiclassical approximation to a Green function is accurate at least to order (Formula presented). For a photon in free space the semiclassical approximation to (Formula presented) and to (Formula presented) happens to be exact, but it is accurate only to first order in (Formula presented) for (Formula presented). The saddle-point approximation to the Laplace transform of (Formula presented) is exact only for (Formula presented), since it is proportional to a (Formula presented) function, i.e., a Gaussian of arbitrarily small width
    • The semiclassical approximation to a Green function is accurate at least to order (Formula presented). For a photon in free space the semiclassical approximation to (Formula presented) and to (Formula presented) happens to be exact, but it is accurate only to first order in (Formula presented) for (Formula presented). The saddle-point approximation to the Laplace transform of (Formula presented) is exact only for (Formula presented), since it is proportional to a (Formula presented) function, i.e., a Gaussian of arbitrarily small width.
  • 26
    • 85037183705 scopus 로고    scopus 로고
    • Note that, not surprisingly, Eq. (2.18) has a one-dimensional form. On setting (Formula presented) the perpendicular components in Eq. (2.16) drop out but, because of reflections (or images), the (Formula presented) components do not. Integration over (Formula presented) is therefore trivial
    • Note that, not surprisingly, Eq. (2.18) has a one-dimensional form. On setting (Formula presented) the perpendicular components in Eq. (2.16) drop out but, because of reflections (or images), the (Formula presented) components do not. Integration over (Formula presented) is therefore trivial.
  • 31
    • 0343205678 scopus 로고
    • SPHDA9 see also V.M. Mostepanenko and N.N. Trunov, The Casimir Effect and its Applications (Oxford University Press, Oxford, 1997), Sec. 3.7, where bounds on the coefficient of the leading term are provided
    • V.M. Mostepanenko and I.Y. Sokolov, Dokl. Akad. Nauk SSSR 298, 1380 (1988) [Sov. Phys. Dokl. 33, 140 (1988)]; SPHDA9see also V.M. Mostepanenko and N.N. Trunov, The Casimir Effect and its Applications (Oxford University Press, Oxford, 1997), Sec. 3.7, where bounds on the coefficient of the leading term are provided.
    • (1988) Sov. Phys. Dokl. , vol.33 , pp. 140
    • Mostepanenko, V.M.1    Sokolov, I.Y.2
  • 32
    • 0004111755 scopus 로고
    • PLRAAN See also P.W. Milonni and M.-L. Shih, Contemporary Physics, edited by J.S. Dougdale (Taylor and Francis, London, 1993)
    • L. Spruch and Y. Tikochinsky, Phys. Rev. A 48, 4213 (1993) use a slightly differet approach. PLRAANSee also P.W. Milonni and M.-L. Shih, Contemporary Physics, edited by J.S. Dougdale (Taylor and Francis, London, 1993).
    • (1993) Phys. Rev. A , vol.48 , pp. 4213
    • Spruch, L.1    Tikochinsky, Y.2
  • 33
    • 0001587411 scopus 로고
    • APNYA6
    • We also note that a number of results for the leading term of the forces between pairs of systems of various geometries have been obtained by J. Blocki, J. Randrup, W.J. Swiatecki, and C.F. Tang, Ann. Phys. (N.Y.) 105, 427 (1977). The approach used was somewhat similar to that used by Derjaguin 8.APNYA6
    • (1977) Ann. Phys. (N.Y.) , vol.105 , pp. 427
    • Blocki, J.1    Randrup, J.2    Swiatecki, W.J.3    Tang, C.F.4


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