On the origin and convergence of a post-quantization constrained propagator for path integral simulations of rigid bodies
Bibliographic record
Abstract
We present a new methodological procedure, based on Post-Quantization Constraints (PQC), to obtain approximate density matrices and energy estimators for use in path integral molecular dynamics and Monte Carlo simulations. The approach serves as a justification of the use of "RATTLE & SHAKE" type methods for path integrals. A thorough discussion of the underlying geometrical concepts is given. Two standard model systems, the particle on a ring and the three-dimensional linear rotor, are used to illustrate and benchmark the approach. In these two cases, matrix elements of the newly defined propagator are explicitly computed in both "angular coordinate" and "angular momentum" bases. A detailed analysis of the convergence properties of the density matrix, and energy estimator with respect to their "exact" counterparts, is presented along with numerical illustrations. We conclude that the use of a PQC-type propagator is justified and practical.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".