Three-dimensional Coupled PT-symmetric Electronic Resonators

TL;DR

This paper theoretically analyzes three-dimensional PT-symmetric coupled electronic resonators, revealing phase transitions, exceptional points, and their implications for wireless power and sensing technologies.

Contribution

It introduces a detailed theoretical framework for high-dimensional PT-symmetric electronic systems, highlighting conditions for exceptional points and phase transitions.

Findings

Identification of two phase transitions in planar configurations

Proposal of a modified exceptional point with approximation conditions

Theoretical insights supporting wireless power and sensing applications

Abstract

In this article, the non-Hermitian characteristics of three-dimensional PT-symmetric coupled electronic resonators are theoretically analyzed. First, the concept of non-Hermitian PT symmetry is illustrated in the context of electronics using a pair of coupled electronic resonators. Two typical configurations of parallel-coupled PT-symmetric electronic trimers are then analyzed. The results indicate that, for the planar configuration, the system can exhibit two phase transitions as the coupling coefficient or gain-loss parameter changes, different from the linear configuration. By comparing system equations based on coupled-mode theory and circuit theory, it is shown that high dimensionality alone is not a sufficient condition for the existence of a higher-order exceptional point; an approximation condition is also required. A modified exceptional point is proposed, and the approximation conditions for the mean deviation $D$ for the real part of the three eigenfrequencies, satisfying $D \leq 1\%$ and $D \leq 0.1\%$, are discussed, respectively. The theoretical results presented in this paper not only reveal the unique non-Hermitian characteristics of high-dimensional PT-symmetric electronic systems but also offer theoretical support for wireless power transmission and wireless sensing technologies.