近日，江西理工大学赵文垒团队观测到在具有不可避免电感耗散的非厄米电路中，本征模在未发生简并的情况下呈现指数增长。2025年11月13日，《物理评论A》杂志发表了这一成果。

研究组从实验和理论两方面研究了增益和损耗RLC谐振器通过电容器耦合的电子电路的本征模。由于电感中不可避免的磁损耗，研究组发现与具有自发PT对称性破缺的传统非厄米系统相比，本征模合并不再出现。特别是，他们发现谐振器的周期性电压振荡幅度从指数衰减到指数增长的转变。

跃迁发生在非厄米电路的异常点附近，而不考虑电感的耗散。研究组引入了一个比RLC谐振器小两个数量级的小电阻来模拟电感器中的能量耗散，并在数值上求解等效的非厄米Schr谔方程。数值结果能很好地再现实验结果。他们的上述发现明确地表明，在异常点以外的指数增长行为是对一些不可避免的耗散扰动的抑制。

附：英文原文

Title: Observing the exponential growth of the eigenmodes in the absence of coalescence for a non-Hermitian circuit with an unavoidable inductor dissipation

Author: Jiaming Zhang, Wenxuan Song, Hanhao Li, Zhiye Kuang, Zhihua Xiong, Longwen Zhou, Jie Liu, Wen-Lei Zhao

Issue&Volume: 2025/11/13

Abstract: We investigate, both experimentally and theoretically, the eigenmodes of an electronic circuit in which gain and loss RLC resonators are coupled through a capacitor. Due to the unavoidable magnetic loss in the inductors, we find that the eigenmode coalescence no longer emerges in contrast to the conventional non-Hermitian systems with spontaneous PT-symmetry breaking. In particular, we find a transition from exponential decay to exponential growth in the amplitude of the periodic voltage oscillations of the resonators. The transition occurs near the exceptional points of the non-Hermitian circuit without considering the dissipations in inductors. We introduce a small resistor two orders of magnitude smaller than that of the RLC resonators to mimic the energy dissipation in inductors and numerically solve the equivalent non-Hermitian Schrdinger equation. The numerical results can well reproduce experimental observations. Our above findings unambiguously indicate that the exponential growth behavior beyond the exceptional points is robust against some unavoidable dissipative perturbations.

DOI: 10.1103/xlbc-w5ng

Source: https://journals.aps.org/pra/abstract/10.1103/xlbc-w5ng