Screening and electronic correlations in quantum wires in strong magnetic fields: Filling factor dependence
Bibliographic record
Abstract
The screening of the Coulomb interaction in quantum wires, subjected to strong perpendicular magnetic fields, is assessed for integer filling factors $\ensuremath{\nu}<~3$ and low temperatures. Correlations due to bulk screening are rather weak whereas those due to screening at the edges are very strong and smoothen considerably the energy dispersion. The group velocity at the Fermi edge ${v}_{g}{(k}_{\mathrm{F}\ensuremath{\nu}})$ can be one order of magnitude larger than the Hartree velocity ${v}_{g}^{\mathrm{H}}{(k}_{\mathrm{F}\ensuremath{\nu}}).$ The exchange-correlation contribution ${v}_{g}^{\mathrm{ec}}{(k}_{\mathrm{F}})$ to ${v}_{g}{(k}_{\mathrm{F}})$ is proved to be nonsingular and for sufficiently strong magnetic fields ${v}_{g}^{\mathrm{ec}}{(k}_{\mathrm{F}})$ is proportional to ${v}_{g}^{\mathrm{H}}{(k}_{\mathrm{F}\ensuremath{\nu}})$ with a proportionality constant that depends on $\ensuremath{\nu}.$ The dispersion relation, obtained in the screened Hartree-Fock approximation, is in line with the observed strong suppression of the spin splitting for $\ensuremath{\nu}=1$ and helps explain the observed destruction or absence of some quantum Hall states. For $\ensuremath{\nu}=2$ the effective ${g}_{\mathrm{op}}^{*}$ factor is constant whereas for $\ensuremath{\nu}=1(3)$ varies strongly across the channel. In addition, the calculated activation energies agree well with those determined experimentally.
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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) | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".