User:Nanite/fluctuation electrodynamics

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Application of fluctuation-dissipation theorem to Maxwell's equations.

Modifies the constitutive relations of materials to include additional random currents and charge densities, whenever and whereever the materials can cause dissipation.

Normally the relation for polarization would be P = (eps-eps_0) E but now becomes P = (eps-eps_0) E + Pnoise. Likewise for magnetization. Pnoise is characterized by a correlation function proportional to imaginary part of eps. (Hmm but actually maybe better to talk in frequency space!)

This full set of Maxwell equations plus constitutive relations then becomes a set of stochastic differential equations, analogous to the Langevin equation. Close link to Johnson noise.

But not only is thermal motion included, also zero point field is included.

History and references according to Volokitin and Persson: "we present a short overview of the basic idea of Rytov’s theory of the fluctuating electromagnetic field ͑Rytov, 1953͒. This theory was originally developed for calculat- ing the thermal electromagnetic field, but is now the ba- sis for theoretical studies of the van der Waals interac- tion ͑Lifshitz, 1956͒, radiative heat transfer ͑Polder and Van Hove, 1971; Loomis and Maris, 1994; Volokitin and Persson, 2001a͒, and van der Waals friction ͑Volokitin and Persson, 1999, 2003c͒ "