On the Problem of van der Waals Forces in Dielectric Media

Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 834)

Abstract

A short review of the problems which arise in the generalization of the Lifshitz theory of van der Waals force in the case of forces inside dielectric media is presented, together with some historical remarks. General properties of the stress tensor of equilibrium electromagnetic field in media are discussed, and the importance of the conditions of mechanical equilibrium is stressed. The physical meaning of the repulsive van der Waals interaction between bodies immersed in a liquid is discussed.

References

  1. 1.
    I use the generic term “van der Waals forces” for long-range forces between neutral objects in any conditions. Thus I do not distinguish between the London, Casimir, Casimir-Polder and Lifshitz forcesGoogle Scholar
  2. 2.
    London, F.: Theory and system of molecular forces. Z. Phys. 63, 245 (1930)ADSMATHCrossRefGoogle Scholar
  3. 3.
    Casimir, H.B., Polder, D.: The influence of retardation on the London-van der Waals forces. Phys. Rev. 73, 360 (1948)ADSMATHCrossRefGoogle Scholar
  4. 4.
    Casimir, H.B.: On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 51, 793 (1948)MATHGoogle Scholar
  5. 5.
    Lifshitz, E.M.: Theory of molecular attraction forces between condensed bodies. Doklady Akademii Nauk SSSR 97, part 4, 643 (1954); Influence of temperature on molecular attraction forces between condensed bodies. 100, part 5, 879 (1955)Google Scholar
  6. 6.
    Lifshitz, E.M.: The theory of molecular attractive forces between solids. Sov. Phys. JETP 2, 73 (1956)MathSciNetGoogle Scholar
  7. 7.
    Rytov, S.M.: Theory of the Electric Fluctuations and Thermal Radiation [in Russian] Publication of Acad. of Sciences of USSR, Moscow (1953), English translation: Air Force Cambridge Research Center, Bedford, MA (1959)Google Scholar
  8. 8.
    Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1960. Russian edition was published in 1957MATHGoogle Scholar
  9. 9.
    Dzyaloshinskii, I.E., Pitaevskii, L.P.: Van der Waals forces in an inhomogeneous dielectric. Sov. Phys. JETP. 9, 1282 (1959)Google Scholar
  10. 10.
    Perel, V.I., Pinskii Ya, M.: Stress tensor for a plasma in a high frequency electromagnetic field with account of collisions. Sov. Phys. JETP. 27, 1014 (1968)ADSGoogle Scholar
  11. 11.
    Pitaevskii, L.P.: Electric forces in a transparent dispersive medium. Sov. Phys. JETP. 12, 1008 (1961)MathSciNetGoogle Scholar
  12. 12.
    Pitaevskii, L.P.: Comment on "Casimir force acting on magnetodielectric bodies embedded in media". Phys. Rev. A. 73, 047801 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    Abrikosov, A.A., Gorkov, L.P., Dzyaloshinskii I.E. (1963) Methods of Quantum Field Theory in Statistical Physics, Prentice-Hall, Englewood CliffsGoogle Scholar
  14. 14.
    Here and below I put \(k_B=1\). Likewise I put \(\hbar=1\) in intermediate equations. I use the CGSE system of electromagnetic units and for simplicity neglect the magnetic properties of media, i.e., put \(\mu=1\) Google Scholar
  15. 15.
    Dzyaloshinskii, I.E., Lifshitz, E.M., Pitaevskii, L.P.: Van der Waals forces in liquid films. Sov. Phys. JETP. 10, 161 (1960)Google Scholar
  16. 16.
    Dzyaloshinskii, I.E., Lifshitz, E.M., Pitaevskii, L.P.: The general theory of van der Waals forces. Adv. Phys. 10, 165 (1961)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Barash Yu, S., Ginzburg, V.L.: Electromagnetic fluctuations in matter and molecular (van der Waals) forces between them. Sov. Phys. Uspekhi. 18, 305 (1975)ADSCrossRefGoogle Scholar
  18. 18.
    Schwinger, J., DeRaad, L.L., Milton, K.A.: Casimir effect in dielectrics. Ann. Phys. (N.Y.) 115, 1 (1978)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Volokitin, A.I., Persson, B.N.P.: Radiative heat transfer between nanostructures. Phys. Rev. B. 63, 205404 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    Pitaevskii, L.P.: Thermal Lifshitz force between an atom and a conductor with small density of carriers. Phys. Rev. Lett. 101, 163202 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Munday, J.N., Capasso, F., Parsegian, A.V.: Measured long-range repulsive Casimir-Lifshitz forces. Nature 457, 170 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Munday, J.N., Capasso, F.: Repulsive Casimir and van der Waals forces: from measurements to future technologies. In: Milton, K.A., Bordag, M. (eds) Quantum Field Theory under the Influence of External Conditions., pp. 127. Word Scientific, New Jersey (2010)Google Scholar
  23. 23.
    Note added in proofs: After this article was submitted, a preprint by Zheng and Narayanaswamy [24] appeared, where the authors independently developed a method based on the "three-boundary geometry." Their results coincide with our Green's functions approach. Google Scholar
  24. 24.
    Zheng, Y., Narayanaswamy, A.: Phys. Rev. A. 83, 042504 (2011); e-print arXiv: 1011.5433ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg  2011

Authors and Affiliations

  1. 1.INO-CNR BEC Center and Dipartimento di FisicaUniversitá di TrentoTrentoItaly
  2. 2.Kapitza Institute for Physical ProblemsRussian Academy of SciencesMoscowRussia

Personalised recommendations