论文标题
直接测量特殊抛物线的拓扑特性
Direct Measurement of Topological Properties of an Exceptional Parabola
论文作者
论文摘要
非热系统可以产生称为特殊点（EPS）的分支奇异性。与Hermitian系统中的奇异性不同，EP的拓扑特性涉及产生判别数（DN）的特征值的绕组，也可以涉及产生浆果阶段的特征向量的自由度。多样性的拓扑不变性也使非冬宫的拓扑学更丰富。在这里，我们研究了由EPS形成的抛物线形轨迹，该轨迹具有理论和声学实验。通过通过测量特征值和本征函数获得DNS和浆果相，我们表明EP轨迹将参数空间赋予了一个非平凡的基本组，该基团由两种非副型LOOP类别组成。我们的发现不仅阐明了异国情调的非温和拓扑，而且还为非铁人拓扑不变的实验表征提供了途径。
Non-Hermitian systems can produce branch singularities known as exceptional points (EPs). Different from singularities in Hermitian systems, the topological properties of an EP can involve either the winding of eigenvalues that produces a discriminant number (DN) or the eigenvector holonomy that generates a Berry phase. The multiplicity of topological invariants also makes non-Hermitian topology richer than its Hermitian counterpart. Here, we study a parabola-shaped trajectory formed by EPs with both theory and acoustic experiments. By obtaining both the DNs and Berry phases through the measurement of eigenvalues and eigenfunctions, we show that the EP trajectory endows the parameter space with a non-trivial fundamental group consisting of two non-homotopic classes of loops. Our findings not only shed light on exotic non-Hermitian topology but also provide a route for the experimental characterization of non-Hermitian topological invariants.
