Edge switch transformation in microwave networks

Vitalii Yunko, Małgorzata Białous, and Leszek Sirko
Phys. Rev. E 102, 012210 – Published 14 July 2020

Abstract

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., νnrν̃nνn+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 {νn}n=1 and {ν̃n}n=1 the spectra of microwave networks before and after the edge switch transformation. We demonstrate that the experimental distribution P(ΔN) of the spectral shift ΔN 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(ΔN) of the spectral shift ΔN agrees, within the experimental uncertainty, with the numerical one.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 31 January 2020
  • Accepted 29 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012210

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Networks

Authors & Affiliations

Vitalii Yunko, Małgorzata Białous, and Leszek Sirko

  • Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 102, Iss. 1 — July 2020

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×