Out-of-time-order correlations in the quasiperiodic Aubry-André model
Bibliographic record
Abstract
We study out-of-time-ordered correlators (OTOC) in a free fermionic model with a quasiperiodic potential. This model is equivalent to the Aubry-Andr\'e model and features a phase transition from an extended phase to a localized phase at a nonzero value of the strength of the quasiperiodic potential. We investigate five different time regimes of interest for out-of-time-ordered correlators: early, wave front, $x={v}_{B}t$, late time equilibration, and infinite time. For the early time regime we observe a power law for all potential strengths. For the precursor time regime preceding the wave front we confirm a recently proposed universal form and use it to extract the characteristic velocity of the wave front for the present model. A Gaussian waveform is observed to work well in the time regime surrounding $x={v}_{B}t$, the wave front arrival time. Our main result is for the late time equilibration regime where we derive a finite time equilibration bound for the OTOC, bounding the correlator's distance from its late time value. The bound impose strict limits on equilibration of the OTOC in the extended regime and is valid not only for the Aubry-Andr\'e model but for any quadratic model. Finally, momentum out-of-time-ordered correlators for the Aubry-Andr\'e model are studied where large values of the OTOC are observed at late times at the critical point.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".