Microscopic treatment of charge and spin response to electromagnetic fields
Bibliographic record
Abstract
We approach the problem of describing the interaction of light and matter from a microscopic, semi-classical perspective, limiting to periodic materials. We partition the charge and current density into contributions associated with the lattice sites. This enables us to introduce a microscopic polarization field that follows from a multipole expansion of the site contributions to the charge density. This describes not only the electric dipole moment per unit volume, but also all higher order electric multipole moments. This same procedure is applied to the site contributions to the current density to obtain the microscopic magnetization field, which captures all magnetic multipole moments. Since electrons are free to move through the lattice, not bound to any particular site, we also introduce a free charge and current density to describe the site-to-site dynamics. By spatially averaging the microscopic fields, we recover the analogous macroscopic fields that appear in the inhomogeneous Maxwell equations. We apply this formalism to determine theoretical expressions for various optical response tensors, which relate the polarization, magnetization, and free current to the electromagnetic fields and their derivatives. Considering the linear response of an insulator, one of our results is the collection of tensors that describe optical activity, which requires considering induced electric quadrupole and magnetic dipole moments, as well as the spatial variation of the electromagnetic field. Beyond those tensors we also obtain an expression for the magnetic susceptibility. Where possible, we show that the results we obtain agree with existing expressions in the literature, when the appropriate limits are taken. We then consider the second order susceptibilities that relate the induced polarization or current density to two components of the electromagnetic field. These susceptibilities can describe a wide range of phenomena due to the mixing of different frequency components of the fields. Usual treatments in the literature are limited to the electric dipole approximation, thus we take this limit and demonstrate that our results reproduce the susceptibility tensors for both insulators and metals in this limit. However, with our approach, the path to considering so called ``forbidden" nonlinear optical processes that go beyond the dipole approximation is clear.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".