Edge switch transformation in microwave networks
| Autor: | Leszek Sirko, Vitalii Yunko, Małgorzata Białous |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Quantum Physics FOS: Physical sciences Spectral shift 01 natural sciences Spectral line 010305 fluids & plasmas Combinatorics Distribution (mathematics) Transformation (function) Quantum graph 0103 physical sciences Symmetry (geometry) 010306 general physics Quantum Physics (quant-ph) Microwave |
| Zdroj: | Physical review. E. 102(1-1) |
| ISSN: | 2470-0053 |
| Popis: | We investigated the spectra of resonances of four-vertex microwave networks simulating both quantum graphs with preserved and with partially violated time-reversal invariance before and after an edge switch operation. We show experimentally that under the edge switch operation, the spectra of the microwave networks with preserved time-reversal symmetry are level-1 interlaced, i.e., ${\ensuremath{\nu}}_{n\ensuremath{-}r}\ensuremath{\le}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}}_{n}\ensuremath{\le}{\ensuremath{\nu}}_{n+r}$, where $r=1$, in agreement with the recent theoretical predictions of Aizenman et al. [M. Aizenman, H. Schanz, U. Smilansky, and S. Warzel, Acta Phys. Pol. A 132, 1699 (2017)]. Here, we denote by ${{{\ensuremath{\nu}}_{n}}}_{n=1}^{\ensuremath{\infty}}$ and ${{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}}_{n}}}_{n=1}^{\ensuremath{\infty}}$ the spectra of microwave networks before and after the edge switch transformation. We demonstrate that the experimental distribution $P(\mathrm{\ensuremath{\Delta}}N)$ of the spectral shift $\mathrm{\ensuremath{\Delta}}N$ is close to the theoretical one. Furthermore, we show experimentally that in the case of the four-vertex networks with partially violated time-reversal symmetry, the spectra are level-1 interlaced. Our experimental results are supplemented by the numerical calculations performed for quantum graphs with violated time-reversal symmetry. In this case, the edge switch transformation also leads to the spectra which are level-1 interlaced. Moreover, we demonstrate that for microwave networks simulating graphs with violated time-reversal symmetry, the experimental distribution $P(\mathrm{\ensuremath{\Delta}}N)$ of the spectral shift $\mathrm{\ensuremath{\Delta}}N$ agrees, within the experimental uncertainty, with the numerical one. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|