Spectral repulsion does not uniquely determine modal exchange in a deformed microwave billiard
- 1Qilu Normal University
Abstract
An avoided crossing is a familiar spectral signature of interaction between nearby modes, but the eigenvalue trajectory alone does not establish whether their modal identities are exchanged. We examine this question in a deformed microwave billiard by comparing finite element eigenvalues and fields. Across 21 screened adjacent level events, the spectral slope is compared with the boundary response obtained from the fields at the event center. For the 11 events whose rotation width can be resolved within the sampled interval, the boundary-derived and overlap-derived widths agree to within about 11%. One event behaves differently: The spectral model predicts substantial modal rotation, while the computed fields change very little and are instead reproduced by the boundary response. Another event shows that the mode that improves the eigenvalue model is not the mode that best restores the field subspace. Spectral repulsion alone is therefore not sufficient to determine modal exchange or the reference subspace required over a finite parameter range.
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BibTeX
@article{zhang2026spectral,
title = {{Spectral repulsion does not uniquely determine modal exchange in a deformed microwave billiard}},
author = {Xiaodong Zhang},
journal = {Physical Review Research},
year = {2026},
month = oct,
doi = {10.1103/k12j-gnhf},
url = {https://link.aps.org/doi/10.1103/k12j-gnhf},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Spectral repulsion does not uniquely determine modal exchange in a deformed microwave billiard
AU - Xiaodong Zhang
PY - 2026
DA - 2026/10/13
JO - Physical Review Research
DO - 10.1103/k12j-gnhf
UR - https://link.aps.org/doi/10.1103/k12j-gnhf
AB - An avoided crossing is a familiar spectral signature of interaction between nearby modes, but the eigenvalue trajectory alone does not establish whether their modal identities are exchanged. We examine this question in a deformed microwave billiard by comparing finite element eigenvalues and fields. Across 21 screened adjacent level events, the spectral slope is compared with the boundary response obtained from the fields at the event center. For the 11 events whose rotation width can be resolved within the sampled interval, the boundary-derived and overlap-derived widths agree to within about 11%. One event behaves differently: The spectral model predicts substantial modal rotation, while the computed fields change very little and are instead reproduced by the boundary response. Another event shows that the mode that improves the eigenvalue model is not the mode that best restores the field subspace. Spectral repulsion alone is therefore not sufficient to determine modal exchange or the reference subspace required over a finite parameter range.
SN - 2643-1564
ER -