Dzyaloshinskii-Lifshitz-Pitaevskii theory

However, it is based on the approximations already discussed in Chapter 4, especially the additivity of pair interactions, which does not hold for London interactions. The alternative Lifshitz theory (Dzyaloshinskii, Lifshitz, and Pitaevskii 1961), based on quantum field theory, treats the large bodies as continuous media, avoiding totally the consideration of atomic structure but using bulk properties such as dielectric permittivity and refractive indices instead. It has been further developed more recently and alternative, simpler treatments have been given (Mahanty and Ninham 1977 Hough and White 1980 Parsegian 2006 Israelachvili 2010). It can be shown that the bulk or volume polarizability of a planar dielectric medium 1 in a medium 3 is given by... 

From 1954 to 1956, Lifshitz derived the theoretical description for the forces betv een two parallel plates of dielectric materials across a vacuum [19]. This theory was extended together with Dzyaloshinskii and Pitaevskii between 1959 and 1961 to include the effect of a third dielectric filling the gap between the plates [20]. However, the complicated structure of their solution hindered its widespread acceptance and initially caused doubt of its practical use [21]. A simplified derivation of the van der Waals forces between parallel plates was introduced by van Kampen et al. [22] based on a model in which the fiuctuations were represented by a sum of harmonic oscillators. Since the bulk modes are independent of distance between the surfaces, only surface modes contribute to the van der Waals force. Based on the van Kampen calculations, Parsegian and Ninham showed in a series of papers in 1970 that the van der Waals forces could be calculated based on available dielectric data [23]. This paned the way for a general quantitative description of van der Waals forces. 

I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevskii, "The general theory of van der Waals forces," Adv. Phys., 10, 165 (1961), for the method, though applied only to a vacuum gap see also Chapter VIII, E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics, Part 2 in Vol. 9 of Course of Theoretical Physics Series (Pergamon, Oxford, 1991) a systematic derivation of the full DLP result is given also in Chap. 6 of A. A. Abrikosov, L. P. Gorkov, Sc I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, R. A. Silverman, trans. (Dover, New York, 1963). 

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