A microscopic study of spin-polarized <sup>40</sup>K atoms in one dimension using the static fluctuation approximation (SFA)
Bibliographic record
Abstract
The thermodynamic and magnetic properties of a spin-mixture of 40K atoms in a 1D harmonic trap, in the presence of an external magnetic field H, are studied using the static fluctuation approximation (SFA). The two-body interaction used is the contact potential. The thermodynamic properties include the chemical potential, energy per particle, specific heat capacity, and entropy per particle. The magnetic properties comprise the magnetization per particle and susceptibility per particle. A phase transition is observed for the repulsive interactions around 0.35TF and 0.5TF in the channels {–9/2, –7/2} and {–9/2, –5/2}, respectively. A peak appears in the entropy and susceptibility at effective scattering length |a1d| ≈ 0.16 μm. For the attractive interactions, three different behaviors depending on H are found in the low-temperature limit. The first behavior is when H < Hc, where Hc is the critical magnetic field, and typical peaks emerge. The second behavior is at H = Hc, and a magnetic phase transition occurs. The third behavior is when H > Hc and the system becomes a partially polarized phase. Our results are consistent with the reported results obtained by the local density approximation, thermal Bethe ansatz method, mean-field approximation, and quantum transfer matrix method.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Open science | 0.000 | 0.000 |
| 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".