Localization and delocalization for strong disorder in one-dimensional continuous potentials
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Bibliographic record
Abstract
In one-dimension and for discrete uncorrelated random potentials, such as\ntight binding models, all states are localized for any disorder strength. This\nis in contrast to continuous random potentials, where we show here that\nregardless of the strength of the random potential, we have delocalization in\nthe limit where the roughness length goes to zero. This result was obtained by\nderiving an expression for the localization length valid for all disorder\nstrengths. We solved a nonlinear wave equation, whose average over disorder\nyields the localization properties of the desired linear wave equation. Our\nresults, not only explain the origin of the difficulty to observe localization\nin certain physical systems, but also show that maximum localization occurs\nwhen the roughness length is comparable to the wavelength, which is relevant\nto many experiments in a random medium.
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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