# A Book Hunt: Statistical Treatment of Macroscopic Maxwell Eqns

1. May 8, 2017

### Twigg

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 $\vec{J}$

2. May 11, 2017

### Baluncore

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.

Use; https://www.bookfinder.com It integrates many new and used book suppliers in one search, including Amazon.
Where possible, buy books from Amazon through the PF link to support this forum.

3. May 12, 2017

### DrDu

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.