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A Book Hunt: Statistical Treatment of Macroscopic Maxwell Eqns

  1. May 8, 2017 #1


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    Hello all,

    Jackson Ch. 6 (3rd edition) tells the reader to look at de Groot for a statistical mechanical derivation of the macroscopic Maxwell equations. I figure he means "Foundations of Electrodynamics" by S. R. de Groot. I requested that book be sent to my school library on loan, but I was wondering in the meanwhile if anyone is familiar with the subject matter and has alternative sources.

    I'm looking for this material for a project. As a final project for my independent study, I am giving a 30 minute talk in which I explain the origin of near-field resonances at subwavelength distances outside a dielectric and paint a clear picture of what happens microscopically, both inside and outside the material. I am focusing my discussion on the content of "Near-Field Spectral Effects due to Electromagnetic Surface Excitations" by A. V. Shchegrov et al, Phys. Rev. Lett. 85, pgs. 1548-51 (2000), which considers thermal currents for source terms. I want to have a slide with the stat. mech. version of Jackson's equation equation 6.96, below in shortened form. By stat. mech. version of this equation, I mean a form in which the averages are done on the ensemble instead of using a spatial kernel.

    $$ \langle j_{\alpha}(\vec{x},t) \rangle = J_{\alpha}(\vec{x},t) + \frac{\partial}{\partial t} [D_{\alpha}(\vec{x},t) - E_{\alpha}(\vec{x},t)] + \epsilon_{\alpha \beta \gamma} \partial_{\beta} M_{\gamma}(\vec{x},t) + \partial_{\beta} \langle \Sigma_{n (molecules)} 2(p_{n})_{[ \alpha}(v_{n})_{\beta ]} \delta(\vec{x} - \vec{x_{n}}) \rangle - \frac{1}{6} \partial_{\beta} \partial_{\gamma} \langle \Sigma_{n (molecules)} 2(v_{n})_{[ \gamma}(Q'_{n})_{\alpha ] \beta} \delta(\vec{x} - \vec{x_{n}}) \rangle + ...$$
    where ##\vec{j}## is the microscopic current as opposed to the macroscopic current ##\vec{J}##

    Thanks in advance!
  2. jcsd
  3. May 11, 2017 #2


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    Sorry, but I can find only one copy of "Foundations of Electrodynamics". By S. R. de Groot. available worldwide. From Zubal Books, Cleveland, Ohio. Hardcover, ISBN 0444103708 Publisher: Noord-Hollandsche U.M, 1972. 535 pages. The used book price is AU$380, about US$275, probably because it is rare.

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  4. May 12, 2017 #3


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    I don't think de Groot is still relevant, if it ever was. The assumption, that a macroscopic object is built up from molecules, which can be treated as independent, is simply not correct beyond classical mechanics or diluted gasses. Take also in mind that Jackson wasn't a solid state physicist, so his presentation of electrodynamcis of continua is not as reliable as the rest of his book.
    I can recommend
    The Dielectric Function of Condensed Systems
    edited by L.V. Keldysh,A.A. Maradudin,D.A. Kirzhnitz

    especially chapters 1 and 4.
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