通过静电类比设计非厄米实能谱

Designing non-Hermitian real spectra through electrostatics

非厄米性的研究蕴涵着诸多新物理机制与现象,在激光与传感等多个方面有着重要的应用价值.在非厄米系统中,实本征能量意味着系统具有稳定性,这一性质可通过奇偶时间(PT)对称性保护,并在不同物理系统中得到广泛的研究.本文利用一种新的动力学机制保证实能谱,提出了一种普适的方案来设计具有实能谱的哈密顿量.该方案基于对扩展非厄米体边对应的静电类比,其中静电荷对应态密度,电场则对应复能谱流.通过这一方案,可以重构出具有任意能谱及态局域性质的哈密顿量,即便这些性质不具备任何对称性特征.通过用泊松边值问题代替原本的非厄米哈密顿量对角化问题,这一静电类比也避免了传统数值方法中因非厄米耗散/增益引起的浮点误差问题,从而允许对更大尺寸的系统进行计算.

Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing.However,only non-Hermitian systems with real eigenenergies are stable,and great efforts have been devoted in designing them through enforcing parity-time(PT)symmetry.In this work,we exploit a lesser-known dynamical mechanism for enforcing real-spectra,and develop a comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra.Our design approach is based on a new electrostatics analogy for modifed non-Hermitian bulk-boundary correspondence,where electrostatic charge corresponds to density of states and electric felds correspond to complex spectral fow.As such,Hamiltonians of any desired spectra and state localization profle can be reverse-engineered,particularly those without any guiding symmetry principles.By recasting the diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem,our electrostatics analogy also transcends the gain/loss-induced compounding of foating-point errors in traditional numerical methods,thereby allowing access to far larger system sizes.