Apparent Low-Energy Scale Invariance in Two-Dimensional Fermi Gases
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Bibliographic record
Abstract
Recent experiments on a 2D Fermi gas find an undamped breathing mode at twice the trap frequency over a wide range of parameters. To understand this seemingly scale-invariant behavior in a system with a scale, we derive two exact results valid across the entire Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS--BEC) crossover at all temperatures. First, we relate the shift of the mode frequency from its scale-invariant value to ${\ensuremath{\gamma}}_{d}\ensuremath{\equiv}(1+2/d)P\ensuremath{-}\ensuremath{\rho}(\ensuremath{\partial}P/\ensuremath{\partial}\ensuremath{\rho}{)}_{s}$ in $d$ dimensions. Next, we relate ${\ensuremath{\gamma}}_{d}$ to dissipation via a new low-energy bulk viscosity sum rule. We argue that 2D is special, with its logarithmic dependence of the interaction on density, and thus ${\ensuremath{\gamma}}_{2}$ is small in both the BCS--BEC regimes, even though $P\ensuremath{-}2\ensuremath{\epsilon}/d$, sensitive to the dimer binding energy that breaks scale invariance, is not.
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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 it