摘要
Abstract
Recent years have witnessed groundbreaking developments in non-Hermitian sys-tems,which transcend the framework of Hermitian operators in conventional quantum mechan-ics to reveal new physical laws inherent in complex eigenvalues and non-Hermitian symmetries.Unlike Hermitian systems,non-Hermitian systems achieve unified description of dynamical evo-lution through the real-imaginary dual structure of complex eigenvalues,manifesting unique phenomena including exceptional points,non-orthogonal eigenstates,and the non-Hermitian skin effect(NHSE).These distinctive properties originate from the non-Hermitian nature of their Hamiltonians,such as pseudo-Hermiticity constraining real spectra,the separation of algebraic-geometric multiplicities in Jordan block structures,and the generalized Brillouin zone theory reconstructing bulk-boundary correspondence.Prototypical models like the Hatano-Nelson model and non-Hermitian Su-Schrieffer-Heeger(SSH)model demonstrate nonreciprocal hopping and topological responses in complex energy spectra,providing paradigmatic plat-forms for understanding NHSE and energy band singularities.In symmetry and topological classification,non-Hermitian systems extend the traditional Altland-Zirnbauer tenfold classi-fication to the 38-fold Bernard-LeClair symmetry classes,encompassing pseudo-Hermiticity,chiral symmetry,and combined conjugation-transposition operations.Topological classifica-tion progresses through dual approaches:K-theory mapping to Hermitian frameworks and homotopy theory analyzing deformation characteristics of complex band manifolds.Future challenges involve developing universal theories for high-dimensional systems,elucidating crys-talline symmetry impacts on classification,and implementing experimental platforms,ulti-mately advancing applications in open quantum systems,nonequilibrium physics,and novel device engineering.关键词
非厄米系统/伪厄米性/Hatano-Nelson模型/非厄米SSH模型/对称性/拓扑相Key words
non-Hermitian systems/pseudo-Hermiticity/Hatano-Nelson model/non-Hermitian SSH model/symmetry/topological phase分类
化学化工
