Exact and asymptotic solutions of the mixed quantum-classical Liouville equation
Bibliographic record
Abstract
In this article, an exact surface-hopping procedure and an approximate asymptotic method for performing molecular dynamics based on a mixed quantum-classical Liouville equation [J. Chem. Phys. 110, 8919 (1999)] for partially Wigner transformed dynamical variables of a coupled quantum subsystem and classical bath are elaborated. The methods are based upon writing the equations of motion in a basis set in which quantum transitions do not alter the classical trajectory, and therefore avoid ad-hoc momentum jump approximations and are free of singular kernels associated with sampling momenta. Results obtained utilizing the new trajectory methods are presented for a model two-level system bilinearly coupled to a classical harmonic oscillator. These results are compared to results obtained from standard methods of performing mixed quantum-classical dynamics. The new methods perform well for the model system over a wide range of initial kinetic energies.
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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".