Correlativity and the origin of the <i>T</i> <sup>2</sup> difference between the BlochGrüneisen law and the Debye law
Bibliographic record
Abstract
To find the origin of the T 2 difference between the BlochGrüneisen law and the Debye law, a resistivity statistical model for ideal metals is presented. In the model, the system is regarded as a phonon system in which all phonons have the same momentum value, i.e., the mean momentum. The principal point of the simplified model is that the electrons located at the Fermi surface are scattered by these mean-momentum phonons. It is found that the electrical resistivity of an ideal metal is directly proportional to the phonon concentration and the square of the phonon mean momentum, which first related the electrical resistivity to the phonon parameters. The theoretical results from the model are consistent with experimental observations that the electrical resistivity is directly proportional to temperature T at high temperatures, and to T 5 at very low temperatures, naturally, this is consistent with the BlochGrüneisen law. It is found by theoretical analyses that the heat capacity of a solid at very low temperatures is only proportional to the phonon concentration. Therefore, the contribution of the square of phonon mean momentum to the electrical resistivity brings about the T 2 difference between the BlochGrüneisen law and the Debye law. PACS Nos.: 72.10.Di, 65.40.Ba
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".