静电球壳中由双曲性诱导的奇异点
Exceptional point induced by hyperbolicity in an electrostatic spherical shell
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中文总结 AI 辅助
本研究发现各向异性核壳纳米粒子的径向静电问题可仅通过双曲性诱导奇异点，该壳层无源无损耗，电场超阈值后会产生热点，为非厄米物理模拟提供新平台。
中文摘要 AI 辅助
奇异点（Exceptional Points, EPs）是本征值与本征矢量均发生合并的非厄米简并点，通常通过平衡增益与损耗或非互易性来实现。本研究表明，各向异性核壳纳米粒子的径向静电问题无需上述任何条件即可实现奇异点。在对数径向坐标下，该问题为柯西-欧拉方程，可映射为阻尼振荡器，等价于两位置的波多-纳尔逊哈密顿量，因此非厄米性是在空间中模拟而非在时间中实现，唯一控制参数为介电各向异性程度ε_t/ε_r。该壳层是无源、互易且无损耗的，但仅通过双曲性即可产生奇异点与非厄米相变。超过双曲性阈值后，壳层内的电场从单调衰减转变为空间振荡，在中间半径处产生热点，可用于调控荧光、强耦合、传感或隐身。更广泛而言，这确立了双曲介质作为无需增益、损耗或非互易性即可模拟非厄米物理的平台。
英文摘要
Exceptional points (EPs) are non--Hermitian degeneracies at which both eigenvalues and eigenvectors coalesce, usually engineered through balanced gain and loss or non--reciprocity. In this work, we show that the radial electrostatic problem of an anisotropic core--shell nanoparticle realizes an EP without any of the alluded conditons. Written in the logarithmic radial coordinate, the problem is a Cauchy--Euler equation that maps onto a damped oscillator and, equivalently, onto a two-site Hatano--Nelson Hamiltonian, so that the non-Hermiticity is emulated in space rather than in time and the sole control parameter is the degree of dielectric anisotropy, $\varepsilon_t/\varepsilon_r$. The shell is passive, reciprocal, and lossless, yet it hosts an EP and a non--Hermitian phase transition governed by hyperbolicity alone. Beyond a hyperbolicity threshold the electric field inside the shell turns from monotonic decay into spatial oscillation, producing hotspots at intermediate radii which can be exploited to tailor fluorescence, strong coupling, sensing, or cloaking. More broadly, this establishes hyperbolic media as a platform to simulate non--Hermitian physics without gain, loss, or non--reciprocity.
