Bibliographic record
Abstract
Scattering off a potential is a fundamental problem in quantum physics. It has been studied extensively with amplitudes derived for various potentials. In this article, we explore a setting with no potentials, where scattering occurs off a junction where many wires meet. We study this problem using a tight-binding discretization of a star graph geometry—one incoming wire and M outgoing wires intersecting at a point. An incoming wave arrives at the junction and scatters. One part is reflected along the same wire, while the rest is transmitted along the others. Remarkably, the reflectance increases monotonically with M, i.e., the greater the number of outgoing channels, the more the particle bounces back. In the M → ∞ limit, the wave is entirely reflected back along the incoming wire. We rationalize this observation by establishing a quantitative mapping between a junction and an on-site potential. To each junction, we assign an equivalent potential that produces the same reflectance. As the number of wires ( M) increases, the equivalent potential also increases. A recent article by one of us has drawn an equivalence between junctions and potentials from the point of view of bound state formation. Our results here show that the same equivalence also holds for scattering amplitudes. We verify our analytic results by simulating wavepacket motion through a junction. We extend the wavepacket approach to two dimensions where analytic solutions cannot be found. An incoming wave travels on a sheet and scatters off a point where many sheets intersect. As in the one-dimensional problem, we assign an equivalent potential to a junction. However, unlike in 1D, the equivalent potential is momentum-dependent. Nevertheless, for any given momentum, the equivalent potential grows monotonically with the number of intersecting sheets. Our findings can be tested in ultracold atom setups and semiconductor structures.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".