Perturbations of circuit evolution matrices with Jordan blocks
Abstract
In our prior studies, we synthesized special circuits with evolution matrices featuring degenerate eigenfrequencies and nontrivial Jordan blocks. The degeneracy of this type is sometimes referred to as exceptional point of degeneracy (EPD). Our focus here is on the simplest of our circuits featuring EPDs that are composed of only two LC-loops coupled by a gyrator. These circuits, when near an EPD state, can be used for enhanced sensitivity applications. With that in mind, we develop here a comprehensive perturbation theory for these simple circuits near an EPD. Using this theory, we propose an approach to sensing, allowing one to benefit from the proximity to an EPD on the one hand when providing for stable operation on the other hand. We also address a broader scope of problems related to perturbations of Jordan blocks and their numerical treatment that allow us to effectively detect proximity to Jordan blocks.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 01, 2021
- Source ID
- 10.1063/5.0039970
Entities
People
- Alexander Figotin
Organizations
- Air Force Office of Scientific Research
- Northrop Grumman
- University of California, Irvine