论文标题
平均时间对称耦合谐振器的严格量子配方
Rigorous Quantum Formulation of Parity-Time Symmetric Coupled Resonators
论文作者
论文摘要
已经提出了带有团块元件的耦合线圈谐振器的RF/Microwave状态中平均时间（PT）对称现象的严格量子公式。线圈谐振器由肿块元素模型描述，该模型由电感器（L），电阻器（R）和电容器（C）组成。对耦合的LRC线圈谐振器系统的严格量子哈密顿量已经通过原始基础的两次转换得出。第一个基础变换旋转原始基础，从而使耦合线圈谐振器的方程式系统的管理矩阵的偏高项还原为常数。然后，第二个基础变换获得了量子哈密顿量，包括对角线有效的复杂频率和异对角耦合项，以及转换的基础。使用获得的量子哈密顿量，可以像往常一样获得耦合线圈谐振器的特征值和特征向量。最后，数值模拟验证了理论的正确性。耦合线圈谐振器的量子公式可以为设计更好的PT对称系统提供更好的指南。
Rigorous quantum formulation of the Parity-Time (PT) symmetry phenomenon in the RF/microwave regime for a coupled coil resonators with lump elements has been presented. The coil resonator is described by the lump-element model that consists of an inductor (L), a resistor (R) and a capacitor (C). Rigorous quantum Hamiltonian for the coupled LRC coil resonators system has been derived through twice basis transforms of the original basis. The first basis transform rotates the original basis such that off-diagonal terms of the governing matrix of the equation system of the coupled coil resonators reduces to constants. Then a second basis transform obtains the quantum Hamiltonian, including the diagonal effective complex frequencies and the off-diagonal coupling terms, together with the transformed basis. With the obtain quantum Hamiltonian, the eigenvalues and eigenvectors of the coupled coil resonators can be obtained as usual as the quantum Hamiltonian. Finally, numerical simulation verifies the correctness of the theory. The quantum formulation of the coupled coil resonators can provide better guideline to design a better PT-symmetric system.
