Dimensional crossover of superfluid <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>He</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>3</mml:mn> </mml:mmultiscripts> </mml:math> in a magnetic field
Bibliographic record
Abstract
Motivated by recent experiments on superfluid $^{3}\mathrm{He}$ in nanoscale-confined geometries, we theoretically investigate the associated phase diagram in a slab geometry and perpendicular magnetic field as the size of confinement is varied. Our analysis is based on minimizing the Ginzburg-Landau free energy for the $3\ifmmode\times\else\texttimes\fi{}3$ matrix superfluid order parameter for three different boundary conditions. We observe a smooth crossover from the phase diagram of the three-dimensional system to the quasi-two-dimensional limit for slab heights of several hundred nanometers and magnetic fields of several kilogauss. We illuminate that, despite the apparent complexity of the underlying equations, many precise numerical and even analytical statements can be made about the phase structure for general values of the coefficients of the free-energy functional, which can in turn be used to constrain or measure these parameters. To guide future experimental studies, we compute the phase diagram in dependence of pressure, temperature, slab height, and magnetic field.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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; both teacher heads agree on what is shown here.
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".