The European Physical Journal C

, Volume 52, Issue 3, pp 701–720 | Cite as

Thermal correction to the Casimir force, radiative heat transfer, and an experiment

  • V.B. Bezerra
  • G. Bimonte
  • G.L. Klimchitskaya
  • V.M. Mostepanenko
  • C. Romero
Regular Article - Theoretical Physics

Abstract

The low-temperature asymptotic expressions for the Casimir interaction between two real metals described by the Leontovich surface impedance are obtained in the framework of thermal quantum field theory. It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude model attains at zero temperature a positive value, which depends on the parameters of a system, i.e., the Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test, whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates. The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer predicted from this impedance is several times less than previous predictions, due to different contributions from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula is discussed. It is concluded that new measurements of radiative heat transfer are required to find the adequate description of a metal in the theory of electromagnetic fluctuations.

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References

  1. 1.
    E.M. Lifshitz, Zh. Eksp. Teor. Fiz. 29, 94 (1956) [Sov. Phys. JETP 2, 73 (1956)]Google Scholar
  2. 2.
    I.E. Dzyaloshinskii, E.M. Lifshitz, L.P. Pitaevskii, Usp. Fiz. Nauk. 73, 381 (1961) [Sov. Phys. Usp. (USA) 4, 153 (1961)]Google Scholar
  3. 3.
    E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Part 2 (Pergamon Press, Oxford, 1980)Google Scholar
  4. 4.
    K. Schram, Phys. Lett. A 43, 283 (1973)CrossRefADSGoogle Scholar
  5. 5.
    P.W. Milonni, The Quantum Vacuum (Academic Press, San Diego, 1994)Google Scholar
  6. 6.
    F. Zhou, L. Spruch, Phys. Rev. A 52, 297 (1995)CrossRefADSGoogle Scholar
  7. 7.
    C. Genet, A. Lambrecht, S. Reynaud, Phys. Rev. A 67, 043811 (2003)CrossRefADSGoogle Scholar
  8. 8.
    M. Bordag, U. Mohideen, V.M. Mostepanenko, Phys. Rep. 353, 1 (2001)MATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    S.K. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997)CrossRefADSGoogle Scholar
  10. 10.
    U. Mohideen, A. Roy, Phys. Rev. Lett. 81, 4549 (1998)CrossRefADSGoogle Scholar
  11. 11.
    G.L. Klimchitskaya, A. Roy, U. Mohideen, V.M. Mostepanenko, Phys. Rev. A 60, 3487 (1999)CrossRefADSGoogle Scholar
  12. 12.
    A. Roy, C.-Y. Lin, U. Mohideen, Phys. Rev. D 60, 111101(R) (1999)ADSGoogle Scholar
  13. 13.
    B.W. Harris, F. Chen, U. Mohideen, Phys. Rev. A 62, 052109 (2000)CrossRefADSGoogle Scholar
  14. 14.
    F. Chen, G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Phys. Rev. A 69, 022117 (2004)CrossRefADSGoogle Scholar
  15. 15.
    T. Ederth, Phys. Rev. A 62, 062104 (2000)CrossRefADSGoogle Scholar
  16. 16.
    F. Chen, U. Mohideen, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. Lett. 88, 101801 (2002)CrossRefADSGoogle Scholar
  17. 17.
    F. Chen, U. Mohideen, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 66, 032113 (2002)CrossRefADSGoogle Scholar
  18. 18.
    G. Bressi, G. Carugno, R. Onofrio, G. Ruoso, Phys. Rev. Lett. 88, 041804 (2002)CrossRefADSGoogle Scholar
  19. 19.
    R.S. Decca, E. Fischbach, G.L. Klimchitskaya, D.E. Krause, D. López, V.M. Mostepanenko, Phys. Rev. D 68, 116003 (2003)CrossRefADSGoogle Scholar
  20. 20.
    R.S. Decca, D. López, E. Fischbach, G.L. Klimchitskaya, D.E. Krause, V.M. Mostepanenko, Ann. Phys. (New York) 318, 37 (2005)MATHCrossRefADSGoogle Scholar
  21. 21.
    G.L. Klimchitskaya, R.S. Decca, E. Fischbach, D.E. Krause, D. López, V.M. Mostepanenko, Int. J. Mod. Phys. A 20, 2205 (2005)CrossRefADSGoogle Scholar
  22. 22.
    R.S. Decca, D. López, E. Fischbach, G.L. Klimchitskaya, D.E. Krause, V.M. Mostepanenko, Phys. Rev. D 75, 077101 (2007)CrossRefADSGoogle Scholar
  23. 23.
    R.S. Decca, D. López, E. Fischbach, G.L. Klimchitskaya, D.E. Krause, V.M. Mostepanenko, Eur. Phys. J. C 51, 963 (2007)CrossRefADSGoogle Scholar
  24. 24.
    F. Chen, U. Mohideen, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 72, 020101(R) (2005)ADSGoogle Scholar
  25. 25.
    F. Chen, U. Mohideen, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 74, 022103 (2006)CrossRefADSGoogle Scholar
  26. 26.
    F. Chen, G.L. Klimchitskaya, V.M. Mostepanenko, U. Mohideen, Phys. Rev. Lett. 97, 170402 (2006)CrossRefADSGoogle Scholar
  27. 27.
    F. Chen, G.L. Klimchitskaya, V.M. Mostepanenko, U. Mohideen, Opt. Express 15, 4823 (2007)CrossRefADSGoogle Scholar
  28. 28.
    H.B. Chan, V.A. Aksyuk, R.N. Kleiman, D.J. Bishop, F. Capasso, Science 291, 1941 (2001)CrossRefADSGoogle Scholar
  29. 29.
    H.B. Chan, V.A. Aksyuk, R.N. Kleiman, D.J. Bishop, F. Capasso, Phys. Rev. Lett. 87, 211801 (2001)CrossRefADSGoogle Scholar
  30. 30.
    E. Buks, M.L. Roukes, Phys. Rev. B 63, 033402 (2001)CrossRefADSGoogle Scholar
  31. 31.
    E.V. Blagov, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. B 71, 235401 (2005)CrossRefADSGoogle Scholar
  32. 32.
    G.L. Klimchitskaya, E.V. Blagov, V.M. Mostepanenko, J. Phys. A Math. Gen. 39, 6481 (2006)MATHCrossRefADSMathSciNetGoogle Scholar
  33. 33.
    M. Bordag, B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. B 74, 205431 (2006)CrossRefADSGoogle Scholar
  34. 34.
    E.V. Blagov, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. B 75, 235413 (2007)CrossRefADSGoogle Scholar
  35. 35.
    J.F. Babb, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 70, 042901 (2004)CrossRefADSGoogle Scholar
  36. 36.
    M. Antezza, L.P. Pitaevskii, S. Stringari, Phys. Rev. A 70, 053619 (2004)CrossRefADSGoogle Scholar
  37. 37.
    A.I. Volokitin, B.N.J. Persson, Phys. Rev. B 63, 205404 (2001)CrossRefADSGoogle Scholar
  38. 38.
    A.I. Volokitin, B.N.J. Persson, Phys. Rev. B 69, 045417 (2004)CrossRefADSGoogle Scholar
  39. 39.
    G. Bimonte, Phys. Rev. Lett. 96, 160401 (2006)CrossRefADSGoogle Scholar
  40. 40.
    C. Genet, A. Lambrecht, S. Reynaud, Phys. Rev. A 62, 012110 (2000)CrossRefADSGoogle Scholar
  41. 41.
    M. Bordag, B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. Lett. 85, 503 (2000)CrossRefADSGoogle Scholar
  42. 42.
    L.S. Brown, G.J. Maclay, Phys. Rev. 184, 1272 (1969)CrossRefADSGoogle Scholar
  43. 43.
    M. Boström, B.E. Sernelius, Phys. Rev. Lett. 84, 4757 (2000)CrossRefADSGoogle Scholar
  44. 44.
    J.S. Høye, I. Brevik, J.B. Aarseth, K.A. Milton, Phys. Rev. E 67, 056116 (2003)CrossRefADSGoogle Scholar
  45. 45.
    V.B. Bezerra, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 65, 052113 (2002)CrossRefADSGoogle Scholar
  46. 46.
    V.B. Bezerra, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 66, 062112 (2002)CrossRefADSGoogle Scholar
  47. 47.
    V.B. Bezerra, G.L. Klimchitskaya, V.M. Mostepanenko, C. Romero, Phys. Rev. A 69, 022119 (2004)CrossRefADSGoogle Scholar
  48. 48.
    M. Boström, B.E. Sernelius, Physica A 339, 53 (2004)CrossRefADSGoogle Scholar
  49. 49.
    I. Brevik, J.B. Aarseth, J.S. Høye, K.A. Milton, Phys. Rev. E 71, 056101 (2005)CrossRefADSGoogle Scholar
  50. 50.
    G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, J. Phys. A Math. Theor. 40, 339(F) (2007)Google Scholar
  51. 51.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. D 72, 085009 (2005)CrossRefADSGoogle Scholar
  52. 52.
    G.L. Klimchitskaya, B. Geyer, V.M. Mostepanenko, J. Phys. A Math. Gen. 39, 6495 (2006)MATHCrossRefADSMathSciNetGoogle Scholar
  53. 53.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 72, 022111 (2005)CrossRefADSGoogle Scholar
  54. 54.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Int. J. Mod. Phys. A 21, 5007 (2006)MATHCrossRefADSMathSciNetGoogle Scholar
  55. 55.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Ann. Phys. (N.Y.) (2007) to appear, DOI 10.1016/j.aop.2007.04.005Google Scholar
  56. 56.
    J.S. Høye, I. Brevik, J.B. Aarseth, K.A. Milton, J. Phys. A Math. Gen. 39, 6031 (2006)CrossRefADSGoogle Scholar
  57. 57.
    V.M. Mostepanenko, V.B. Bezerra, R.S. Decca, E. Fischbach, B. Geyer, G.L. Klimchitskaya, D.E. Krause, D. López, C. Romero, J. Phys. A Math. Gen. 39, 6589 (2006)CrossRefADSGoogle Scholar
  58. 58.
    L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon Press, Oxford, 1984)Google Scholar
  59. 59.
    E.I. Kats, Zh. Eksp. Teor. Fiz. 73, 212 (1977) [Sov. Phys. JETP 46, 109 (1977)]Google Scholar
  60. 60.
    V.B. Bezerra, G.L. Klimchitskaya, C. Romero, Phys. Rev. A 65, 012111 (2002)CrossRefADSGoogle Scholar
  61. 61.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 67, 062102 (2003)CrossRefADSGoogle Scholar
  62. 62.
    V.B. Svetovoy, M.V. Lokhanin, Phys. Rev. A 67, 022113 (2003)CrossRefADSGoogle Scholar
  63. 63.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. A 70, 016102 (2004)CrossRefADSGoogle Scholar
  64. 64.
    J.R. Torgerson, S.K. Lamoreaux, Phys. Rev. E 70, 047102 (2004)CrossRefADSGoogle Scholar
  65. 65.
    G. Bimonte, Phys. Rev. E 73, 048101 (2006)CrossRefADSGoogle Scholar
  66. 66.
    J.R. Torgerson, S.K. Lamoreaux, Phys. Rev. E 73, 048102 (2006)CrossRefADSGoogle Scholar
  67. 67.
    D. Polder, M. Van Hove, Phys. Rev. B 4, 3303 (1971)CrossRefADSGoogle Scholar
  68. 68.
    J.J. Loomis, H.J. Maris, Phys. Rev. B 50, 18517 (1994)CrossRefADSGoogle Scholar
  69. 69.
    V.M. Mostepanenko, N.N. Trunov, The Casimir Effect and its Applications (Clarendon Press, Oxford, 1997)Google Scholar
  70. 70.
    T. Emig, R. Büscher, Nucl. Phys. B 696, 468 (2004)MATHCrossRefADSGoogle Scholar
  71. 71.
    E.M. Lifschitz, L.P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, 1981)Google Scholar
  72. 72.
    G.L. Klimchitskaya, V.M. Mostepanenko, Phys. Rev. B 75, 036101 (2007)CrossRefADSGoogle Scholar
  73. 73.
    V.B. Bezerra, R.S. Decca, E. Fischbach, B. Geyer, G.L. Klimchitskaya, D.E. Krause, D. López, V.M. Mostepanenko, C. Romero, Phys. Rev. E 73, 028101 (2006)CrossRefADSGoogle Scholar
  74. 74.
    I. Brevik, J.B. Aarseth, J. Phys. A Math. Gen. 39, 6187 (2006)CrossRefADSMathSciNetGoogle Scholar
  75. 75.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1976)Google Scholar
  76. 76.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1994)MATHGoogle Scholar
  77. 77.
    B. Geyer, G.L. Klimchitskaya, V.M. Mostepanenko, Int. J. Mod. Phys. A 16, 3291 (2001)CrossRefADSGoogle Scholar
  78. 78.
    C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996)Google Scholar
  79. 79.
    L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1 (Pergamon, Oxford, 1980)Google Scholar
  80. 80.
    J. Feinberg, A. Mann, M. Revzen, Ann. Phys. (New York) 288, 103 (2001)MATHCrossRefADSMathSciNetGoogle Scholar
  81. 81.
    A. Scardicchio, R.L. Jaffe, Nucl. Phys. B 743, 249 (2006)MATHCrossRefADSMathSciNetGoogle Scholar
  82. 82.
    E.D. Palik (Ed.), Handbook of Optical Constants of Solids (Academic, New York, 1985)Google Scholar
  83. 83.
    A. Lambrecht, S. Reynaud, Eur. Phys. J. D 8, 309 (2000)CrossRefADSGoogle Scholar
  84. 84.
    G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Phys. Rev. A 61, 062107 (2000)CrossRefADSGoogle Scholar
  85. 85.
    M. Boström, B.E. Sernelius, Phys. Rev. A 61, 046101 (2000)CrossRefADSGoogle Scholar
  86. 86.
    S.M. Rytov, Theory of Electric Fluctuations and Thermal Radiation (Air Force Cambridge Research Center, Bedford, Mass., 1959)Google Scholar
  87. 87.
    M.A. Leontovich, S.M. Rytov, Zh. Eksp. Teor. Fiz. 23, 246 (1952)Google Scholar
  88. 88.
    C.M. Hargreaves, Phys. Lett. A 30, 491 (1969)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2007

Authors and Affiliations

  • V.B. Bezerra
    • 1
  • G. Bimonte
    • 2
    • 3
  • G.L. Klimchitskaya
    • 4
  • V.M. Mostepanenko
    • 4
  • C. Romero
    • 1
  1. 1.Department of PhysicsFederal University of ParaíbaJoão PessoaBrazil
  2. 2.Dipartimento di Scienze FisicheUniversità di Napoli Federico II, Complesso Universitario MSANapoliItaly
  3. 3.INFN, Sezione di NapoliNapoliItaly
  4. 4.Center of Theoretical Studies and Institute for Theoretical PhysicsLeipzig UniversityLeipzigGermany

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