Quantum reaction rates and sampling of quantum equilibrium structure
Bibliographic record
Abstract
The time dependent quantum reaction rate may be expressed in terms of the Kubo-transformed reactive flux correlation function involving the Kubo-transformed quantum spectral density function W¯A(X,0). The rate constant, which is obtained from the long time limit of this correlation function, can also be expressed in terms of a simple quantum canonical correlation function. In this context, two useful alternative expressions, WA(X,iℏβ/2) and ReWA(X,0), to the difficult-to-compute W¯A(X,0) function are compared. The spectral density WA(X,iℏβ/2) is a real and symmetric approximation to W¯A(X,0) while ReWA(X,0) is a much simpler form obtained from the quantum canonical correlation function. Computations on a simple parabolic barrier crossing problem and a two-level system reactive system confirm that the long time reaction rate constant is the same for all spectral density expressions. Our results show that the density function WA(X,iℏβ/2) may be more suitable for simple model systems while ReWA(X,0) may be more useful for complicated systems involving many degrees of freedom.
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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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".