On the calculation of single-particle time correlation functions from Bose–Einstein centroid dynamics
Bibliographic record
Abstract
The calculation of single-particle time correlation functions using the Bose-Einstein centroid dynamics formalism is discussed. A new definition of the quasidensity operator is used to calculate the centroid force on a given particle for an anharmonic system. The force includes correlation effects due to quantum statistics and is used for the calculation of the classical-like dynamics of phase-space centroid variables within the centroid molecular dynamics approximation. Time correlation functions are then obtained for single-particle quantities. These correspond to the double-Kubo transform of exact quantum-mechanical correlation functions. The centroid dynamics results are compared to those of exact basis-set calculations and a good agreement is found. The level of accuracy is in fact the same as what was observed earlier for the calculation of center-of-mass correlation functions for Fermi-Dirac and Bose-Einstein statistics, and for any correlation function for Boltzmann statistics. These results show that it is now possible to use Bose-Einstein centroid molecular dynamics to calculate single-particle correlation functions for systems where quantum exchange effects are present.
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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".