Fractional quantization of Hall resistance as a consequence of\n mesoscopic feedback
Bibliographic record
Abstract
A nonlinear single-particle model is introduced, which captures the\ncharacteristic of systems in the quantum Hall regime. The model entails the\nmagnetic Shr\\"odinger equation with spatially variable magnetic flux density.\nThe distribution of flux is prescribed via the postulates of the mesoscopic\nmechanics (MeM) introduced in my previous articles [cf. J. Phys. Chem. Solids,\n65 (2004), 1507-1515; J. Geom. Phys., Vol. 55/1 (2005), 1-18]. The model is\nfound to imply exact integer and fractional quantization of the Hall\nconductance. In fact, Hall resistance is found to be $R_H =\n\\frac{h}{2e^2}\\frac{M}{N}$ at the filling factor value $N/M$. The assumed\ngeometry of the Hall plate is rectangular. Special properties of the magnetic\nShr\\"odinger equation with the mesoscopic feedback loop allow us to demonstrate\nquantization of Hall resistance as a direct consequence of charge and flux\nquantization. I believe results presented here shed light at the overall status\nof the MeM in quantum physics, confirming its validity.\n
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".