Solutions of mixed quantum-classical dynamics in multiple dimensions using classical trajectories
Bibliographic record
Abstract
The multithreads algorithm for solving the mixed quantum-classical Liouville equation is extended to systems in which multiple classical degrees of freedom couple explicitly to a quantum subsystem. The method involves evolving a discrete set of matrices representing operators positioned at classical phase space coordinates according to precise dynamical rules dictated by evolution equations. The propagation scheme is based on the Trotter expansion of the time evolution operator and involves trajectory (thread) branching and pruning operations at each time step. The method is tested against exact numerical solution of the quantum dynamics for two models in which the nonadiabatic evolution of two heavy coordinates (nuclei) induces changes in population in two electronic states. It is demonstrated that the multithreads algorithm provides a good quantitative as well as qualitative description of the dynamics for branching ratios and populations as a function of time. Critical performance issues such as the computational demand of the method, energy conservation, and how the scheme scales with the number of classical degrees of freedom coupled to the quantum subsystem are discussed.
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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 | 0.001 |
| 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".