光学势中自对偶谱奇异性分裂引起的相变
Phase transition through the splitting of self-dual spectral singularity in optical potentials
摘要：
我们考虑具有反线性对称性的光学介质。我们证明：（i）这种介质的谱奇点（如果有的话）总是自对偶的，即，对应于CPA激光器;（ii）在系统参数变化的情况下，自对偶谱奇异性可能分裂成一对孤立的复共轭本征值，这对应于相变的一个非常规的和在大多数以前的研究中被忽视的情况（称为$PT$ --在服从宇称时间对称的系统中的对称性破缺）;（iii）如果反线性对称是局部的，即，不涉及任何空间反射，则不可能有光谱奇异性。我们的研究结果说明了几个例子，包括$PT$对称双层和其他复杂的潜力在最近的文献中讨论。
英文摘要：
We consider optical media which feature antilinear symmetries. We show that: (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to CPA-lasers; (ii) under the change of a system's parameter the self-dual spectral singularity may split into a pair of isolated complex conjugate eigenvalues, which corresponds to an unconventional and overlooked in the most of previous studies scenario of the phase transition (known as $PT$-symmetry breaking in systems obeying parity-time symmetry); (iii) if the antilinear symmetry is local, i.e., does not involve any spatial reflection, then no spectral singularity is possible. Our findings are illustrated with several examples including a $PT$-symmetric bilayer and other complex potentials discussed in recent literature.
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