论文标题
超对称阵列中的高阶特殊点
High-order exceptional points in supersymmetric arrays
论文作者
论文摘要
我们采用交织的操作员技术来合成任意尺寸$ n $的超对称（SUSY）阵列。合成的SUSY系统等于在有效的磁场下的自旋-（N-1）/2 $。通过考虑一个额外的假想磁场，我们获得了广义的平价时间对称非对称的非热汉顿式汉密尔顿，该磁场描述了在梯度增益和损失下的Susy耦合共振器或波导阵列；所有$ n $能量水平在特殊点（EP）结合在一起，形成各向同性高阶EP，$ n $ State Colescence（EPN）。在EPN附近，每个特征态的相位刚度的缩放指数为$（n-1）/2 $；对扰动$ε$作用在谐振器或波导耦合上的特征频率响应为$ε^{1/n} $。我们的发现揭示了交织操作员技术对频谱工程的重要性，并示了非武术物理学中的实际应用。
We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size $N$. The synthesized SUSY system is equivalent to a spin-$(N-1)/2$ under an effective magnetic field. By considering an additional imaginary magnetic field, we obtain a generalized parity-time-symmetric non-Hermitian Hamiltonian that describes a SUSY array of coupled resonators or waveguides under a gradient gain and loss; all the $N$ energy levels coalesce at an exceptional point (EP), forming the isotropic high-order EP with $N$ states coalescence (EPN). Near the EPN, the scaling exponent of phase rigidity for each eigenstate is $(N-1)/2$; the eigen frequency response to the perturbation $ε$ acting on the resonator or waveguide couplings is $ε^{1/N}$. Our findings reveal the importance of the intertwining operator technique for the spectral engineering and exemplify the practical application in non-Hermitian physics.
