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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!
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!