One plus two-body random matrix ensembles with parity: Density of states and parity ratios
Bibliographic record
Abstract
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [$\mathrm{EGOE}(1+2)\ensuremath{-}\ensuremath{\pi}$] generated by a random two-body interaction (modeled by GOE in two-particle spaces) in the presence of a mean field for spinless identical fermion systems is defined, generalizing the two-body ensemble with parity analyzed by Papenbrock and Weidenm\"uller [Phys. Rev. C 78, 054305 (2008)], in terms of two mixing parameters and a gap between the positive $(\ensuremath{\pi}=+)$ and negative $(\ensuremath{\pi}=\ensuremath{-})$ parity single-particle (sp) states. Numerical calculations are used to demonstrate, using realistic values of the mixing parameters appropriate for some nuclei, that the $\mathrm{EGOE}(1+2)\ensuremath{-}\ensuremath{\pi}$ ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue densities (i.e., state densities). The random matrix model also generates many features in parity ratios of state densities that are similar to those predicted by a method based on the Fermi-gas model for nuclei. We have also obtained, by applying the formulation due to Chang et al. [Ann. Phys. (NY) 66, 137 (1971)], a simple formula for the spectral variances defined over fixed-$({m}_{1},{m}_{2})$ spaces, where ${m}_{1}$ is the number of fermions in the positive parity sp states and ${m}_{2}$ is the number of fermions in the negative parity sp states. Similarly, using the binary correlation approximation, in the dilute limit, we have derived expressions for the lowest two-shape parameters. The smoothed densities generated by the sum of fixed-$({m}_{1},{m}_{2})$ Gaussians with lowest two-shape corrections describe the numerical results in many situations. The model also generates preponderance of positive parity ground states for small values of the mixing parameters, and this is a feature seen in nuclear shell-model results.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".