Comparison of a direct measure of barrier crossing times with indirect measures such as the Larmor time
Bibliographic record
Abstract
Abstract Different approaches for considering barrier crossing times are analyzed, with special emphasis on recent experiments which attempt to measure what is commonly referred to as the Larmor tunneling time. We show that that these experiments cannot reveal the Larmor time, due to the finite energy width of the incident particles. The Larmor time, which measures changes in spin polarization, is classified together with other measurements such as the Buttiker–Landauer oscillating barrier time as indirect measurements of interaction times of scattered particles. In contrast, we present a direct quantum mechanical measure of a barrier crossing time taken to be the difference between the mean flight time for a particle transmitted through a potential barrier incident on a screen and the time it would take to reach the same screen without the barrier. These metrics are asymptotic, in the sense that they infer a time from a measurement after the scattering event is over, whereas other measures like the dwell time are local. Some time measures are well-defined only for incident states which are monochromatic in energy, others are well-defined also for incident wavepackets whose incident energy width is finite. In this paper we compare the different approaches to conclude that only the flight time can be used to answer the provocative (but ultimately ill-posed) question: how much time does it take to tunnel through a barrier?
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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 | 0.000 | 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".