On the correct formula for the lifetime broadened superconducting density of states
Bibliographic record
Abstract
We argue that the well known Dynes formula [Dynes R C {\it et al.} 1978 {\it Phys. Rev. Lett.} {\bf 41} 1509] for the superconducting quasiparticle density of states, which tries to incorporate the lifetime broadening in an approximate way, cannot be justified microscopically for conventional superconductors. Instead, we propose a new simple formula in which the energy gap has a finite imaginary part $-\Delta_2$ and the quasiparticle energy is real. We prove that in the quasiparticle approximation 2$\Delta_2$ gives the quasiparticle decay rate at the gap edge for conventional superconductors. This conclusion does not depend on the nature of interactions that cause the quasiparticle decay. The new formula is tested on the case of a strong coupling superconductor Pb$_{0.9}$Bi$_{0.1}$ and an excellent agreement with theoretical predictions is obtained. While both the Dynes formula and the one proposed in this work give good fits and fit parameters for Pb$_{0.9}$Bi$_{0.1}$, only the latter formula can be justified microscopically.
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 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) | 0.000 | 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 | 0.001 |
| 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 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".