Topological Casimir effect in a quantum LC circuit: Real-time dynamics
Bibliographic record
Abstract
We study novel contributions to the partition function of the Maxwell system defined on a small compact manifold $\mathbb{M}$ with nontrivial mappings ${\ensuremath{\pi}}_{1}[U(1)]\ensuremath{\cong}\mathbb{Z}$. These contributions cannot be described in terms of conventional physical propagating photons with two transverse polarizations and instead emerge as a result of tunneling transitions between topologically different but physically identical vacuum winding states. We argue that if the same system is considered in the background of a small external time-dependent electromagnetic field, then real physical photons will be emitted from the vacuum, similar to the dynamical Casimir effect where photons are radiated from the vacuum due to time-dependent boundary conditions. The fundamental technical difficulty for such an analysis is that the radiation of physical photons on mass shell is inherently a real-time Minkowskian phenomenon while the vacuum fluctuations interpolating between topological $|k⟩$ sectors rest upon a Euclidean instanton formulation. We overcome this obstacle by introducing auxiliary topological fields, which allows for a simple analytical continuation between Minkowski and Euclidean descriptions, and develop a quantum mechanical technique to compute these effects. We also propose an experimental realization of such small effects using a microwave cavity with appropriate boundary conditions. Finally, we comment on the possible cosmological implications of this effect.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".