Self-consistent modification to the electron density of states due to electron-phonon coupling in metals
Bibliographic record
Abstract
The ``standard'' theory of a normal metal consists of an effective electron band which interacts with phonons and impurities. The effects due to the electron-phonon interaction are often delineated within the Migdal approximation; the properties of many simple metals are reasonably well described with such a description. On the other hand, if the electron-phonon interaction is sufficiently strong, a polaron approach is more appropriate. The purpose of this paper is to examine to what degree the Migdal approximation is self-consistent, as the coupling strength increases. We find that changes in the electron density of states become significant for very large values of the coupling strength; however, there is no critical value, nor even a crossover regime where the Migdal approximation has become inconsistent. Moreover, the extent to which the electron band collapses is strongly dependent on the detailed characteristics of the phonon spectrum.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".