Particle dynamics in a virtual harmonic potential
Bibliographic record
Abstract
Feedback traps can create arbitrary virtual potentials for exploring the dynamics of small Brownian particles. In a feedback trap, the particle position is measured periodically and, after each measurement, one applies the force that would be produced by the gradient of the “virtual potential,” at the particle location. Virtual potentials differ from real ones in that the feedback loop introduces dynamical effects not present in ordinary potentials. These dynamical effects are caused by small time scales associated with the feedback, including the delay between the measurement of a particle’s position and the feedback response, the feedback response that is applied for a finite update time, and the finite camera exposure from integrating motion. Here, we characterize the relevant experimental parameters and compare to theory the observed power spectra and variance for a particle in a virtual harmonic potential. We show that deviations from the dynamics expected of a continuous potential are measured by the ratio of these small time scales to the relaxation time scale of the virtual potential.
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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 | 0.000 | 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 | 0.001 | 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".