Energy and shape relaxation in binary atomic systems with realistic quantum cross sections
Bibliographic record
Abstract
We use the spatially homogeneous linear Boltzmann equation to study the time evolution of an initial non-equilibrium distribution function of an ensemble of test particles dilutely dispersed in a background gas at thermal equilibrium. The systems considered are energetic N in He and Xe in He. We employ the quantum mechanical differential cross section to define the collision operator in the Boltzmann equation. The Boltzmann equation is solved with a moment method based on the expansion of the distribution function in the Sonine (Laguerre) polynomials as well as with a direct simulation Monte Carlo method. The moment method provides the approximate eigenvalues and eigenfunctions of the linear Boltzmann collision operator. The reciprocal of the eigenvalues is a measure of the relaxation times to equilibrium. For hard sphere cross sections, the relaxation of the average energy and the shape of the distribution function can be characterized by a single time scale determined by the momentum transfer cross section. We show that this is also the case for realistic quantum cross sections with dominant small angle scattering contributions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".