Equation of state and the Hugoniot of laser shock-compressed deuterium: Demonstration of a basis-function-free method for quantum calculations
Bibliographic record
Abstract
In most density functionals the energy is a functional of the electron density $n(\stackrel{\ensuremath{\rightarrow}}{r})$ and a function of the nuclear positions ${R}_{i}.$ We consider, a functional of both$n(\stackrel{\ensuremath{\rightarrow}}{r})$ and the nuclear density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{r})=\ensuremath{\sum}\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r}\ensuremath{-}{R}_{i}).$ In reducing the two Kohn--Sham equations, a classical mapping valid for interacting electrons is invoked. The exchange-correlation is nonlocal and free of self-interaction errors. As a challenging application, we calculate the equation of state and the shock Hugoniot of deuterium relevant to topical shock experiments. The calculated Hugoniot is quite close to the SESAME and path-integral Monte Carlo Hugoniots. We also treat the nonequilibrium case, which is extremely difficult for standard methods. Here the ${\mathrm{D}}^{+}$ are assumed to be hotter than the electrons, and lead to the soft Hugoniots similar to those seen in the laser-shock data. The softening arises from hot ${\mathrm{D}}^{+}--e$ pairs occurring close to the zero of the electron chemical potential.
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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) | 0.001 | 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".