The transition from the classical to the quantum regime for rubidium-87 (<sup>87</sup>Rb) vapor in terms of the second virial coefficient and the scattering length
Bibliographic record
Abstract
This work focuses on two major properties of 87 Rb gas for a very broad temperature range of ∼nK–3000 K. The first is the second virial coefficient B, encompassing both classical ( B cl ) and quantum ( B q ) regimes as well as, in between, the classical coefficient plus the first quantum correction ( B qcl ). The transition from the classical to the quantum regime in this system is explored. The second property is the s-wave scattering length a 0 for both singlet [[Formula: see text]] and triplet [[Formula: see text]] states. The medium is incorporated into the picture via the Galitskii–Migdal–Feynman formalism. Its main output is the medium phase shifts for the system, using the “best” available interatomic potential. These are plugged into the Beth–Uhlenbeck formula to give B q , whereas B c l and B qcl are readily calculated from standard expressions, the only input needed being the binary potential. Our results show that B q exhibits clear demarcation from B cl , especially at nK temperatures where Bose–Einstein condensation (BEC) manifests itself. Comparison to other calculations in the literature is made only for B cl ; B q for this gas is computed here for the first time, as are [Formula: see text] and [Formula: see text] for the medium. It turns out that these scattering lengths are larger than their vacuum counterparts at BEC temperatures.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".