Scaling and universality in Brownian motion on a stochastic harmonic oscillator chain
Bibliographic record
Abstract
Diffusion of a Brownian particle along a stochastic harmonic oscillator chain is investigated. In contrast to the usually discussed Brownian motion driven by Gaussian white noise, the particle at high temperatures performs long L\'evy flights. At high temperatures $T$ the diffusion coefficient scales as $D\ensuremath{\sim}{T}^{2+\ensuremath{\alpha}}$, where the parameter $\ensuremath{\alpha}$ determine the average damping force $\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}1/({T}^{\ensuremath{\alpha}}P)$ on the particle at large momentum $P$ and at high temperature. The exponent $\ensuremath{\alpha}$ depends on the particle-chain interaction and chain properties. It is shown that the mean time ${\overline{t}}_{f}$ necessary to perform a flight of $l$ lattice constant scales with $l$ as ${\overline{t}}_{f}\ensuremath{\propto}{l}^{2/3}$ at high temperatures and flight lengths. Last, the flight length probability distribution is found to decay as $1/{l}^{\ensuremath{\beta}}$ with the exponent $\ensuremath{\beta}=4/3$ being universal, i.e., independent of the model parameters.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".