Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time
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Bibliographic record
Abstract
In this paper we propose a generalization of the hybrid model for semiconductors already discussed by Chiarelli et al.and Di Michele et al., including a non-constant pressure functional and relaxation time. Roughly speaking, we assume that the normalized electron temperature and the relaxation time in the classical and quantum domains are different from each other. We derive the model heuristically, introducing a generalization of the stress tensor, which accounts for an interface contribute, and afterwards we prove the existence and uniqueness of weak solutions for such a new hybrid model. We apply the approach proposed by Di Michele et al. to obtain the stationary solutions to our problem, namely we prove the existence of the solution for a regularized problem, then we achieve the existence of a weak solution for the hybrid problem as a proper limit of the regular solution previously obtained.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
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 it