观测具有不可避免电感耗散的非厄米电路中无合并情况下本征模的指数增长
Observing the exponential growth of the eigenmodes in the absence of coalescence for a non-Hermitian circuit with an unavoidable inductor dissipation
AI总结：
本文通过实验和理论研究了含电感耗散的非厄米耦合RLC电路，发现本征模合并不再出现，但在奇异点附近仍发生从指数衰减到指数增长的转变，证明该增长行为对耗散扰动具有鲁棒性。
摘要：
我们从实验和理论两方面研究了一种电子电路的本征模，其中增益和损耗RLC谐振器通过电容器耦合。由于电感器中不可避免的磁损耗，我们发现与具有自发PT对称破缺的传统非厄米系统相比，本征模合并不再出现。特别地，我们发现谐振器周期性电压振荡的幅度发生了从指数衰减到指数增长的转变。该转变发生在未考虑电感器耗散的非厄米电路的奇异点附近。我们引入一个比RLC谐振器小三个数量级的小电阻来模拟电感器中的能量耗散，并数值求解等效的非厄米薛定谔方程。数值结果能够很好地重现实验观测。上述发现明确表明，奇异点之外的指数增长行为对某些不可避免的耗散扰动具有鲁棒性。
英文摘要：
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 the spontaneous $\cal{PT}$-symmetry breaking. In particular, we find a transition from the 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 of three orders of magnitude smaller than that of the $RLC$ resonators to mimic the energy dissipation in inductors and numerically solve the equivalent non-Hermitian Schr{\" o}dinger 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.
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