Superfluid phase transition of nanoscale-confined helium-3
Bibliographic record
Abstract
We investigate theoretically the superfluid phase transition of helium-3 under nanoscale confinement of one spatial dimension realized in recent experiments. Instead of the $3\ifmmode\times\else\texttimes\fi{}3$ complex matrix order parameter found in the three-dimensional system, the quasi-two-dimensional superfluid is described by a reduced $3\ifmmode\times\else\texttimes\fi{}2$ complex matrix. It features a nodal quasiparticle spectrum, regardless of the value of the order parameter. The origin of the $3\ifmmode\times\else\texttimes\fi{}2$ order parameter is first illustrated via the two-particle Cooper problem, where Cooper pairs in the ${p}_{x}$ and ${p}_{y}$ orbitals are shown to have a lower bound-state energy than those in ${p}_{z}$ orbitals, hinting at their energetically favorable role at the phase transition. We then compute the Landau free energy under confinement within the mean-field approximation and show that the critical temperature for condensation of the $3\ifmmode\times\else\texttimes\fi{}2$ order parameter is larger than for other competing phases. Through exact minimization of the mean-field free energy, we show that mean-field theory predicts precisely two energetically degenerate superfluid orders to emerge at the transition that are not related by symmetry: The A-phase and the planar phase. Beyond the mean-field approximation, we show that strong-coupling corrections favor the A-phase observed in experiment, whereas weak-coupling perturbative renormalization group predicts the planar phase to be stable.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.003 |
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".