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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| 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 source (direct Gemma or distilled Codex), 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".