A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose–Einstein condensates
Bibliographic record
Abstract
Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose–Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations (‘ground states’) that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result illustrating that vortex polygons in the form of a ring are unstable for N ≥7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases of N =2,…,5. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-called N +1 configuration). We finally examine the opposite limit of large N and illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.
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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) | 0.000 | 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".