Miloslav Znojil
A compact review is given, and a few new numerical results are added to the recent studies of the q-pointed one-dimensional star-shaped quantum graphs. These graphs are assumed endowed with certain specific, manifestly non-Hermitian point interactions, localized either in the inner vertex or in all of the outer vertices and carrying, in the latter case, an interesting zero-inflow interpretation.
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We propose a non-Hermitian generalization of stimulated Raman adiabatic passage (STIRAP), which allows one to increase speed and fidelity of the adiabatic passage. This is done by adding balanced imaginary (gain/loss) terms in the diagonal (bare energy) terms of the Hamiltonian and choosing them such that they cancel exactly the nonadiabatic couplings, providing in this way an effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed Gaussian-shaped pulses in the counter-intuitive scheme the imaginary terms of the Hamiltonian turn out to be time independent. A possible physica…
Implementing non-Abelian Hatano-Nelson model in electric circuits
本文提出非阿贝尔Hatano-Nelson模型，利用非 reciprocal U(2) gauge field 实现Hopf-link状复能量辫形和双极皮肤效应，通过电路实验验证了非赫米特物理的新现象。
Non-Hermitian ring-shaped discrete lattices share the appeal with their more popular linear predecessors. Their dynamics controlled by the nearest-neighbor interaction is equally phenomenologically interesting. In comparison, the innovative nontriviality of their topology may be expected to lead to new spectral effects. Some of them are studied here via solvable examples. Main attention is paid to the perturbation-caused removals of spectral degeneracy at exceptional points.
Many-Body Mobility Edge and Non-Hermitian Skin Effect in an Interacting Quasi-Periodic Spin Chain
本研究探究受准周期纵向场的相互作用非厄米自旋链，发现“D形”多体迁移率边，揭示其与多体皮肤效应的关联，绘制统一相图并明确其在开放量子多体系统物理中的关键作用。
Scale-tailored localization and its observation in non-Hermitian electrical circuits
该研究提出由长程非对称耦合导致的尺度定制局域化，揭示其模式数与局域长度仅随耦合范围标度，并在非厄米电路中完成实验观测。
Bulk spectra and the non-Hermitian skin effect in systems with long-range couplings
研究长程耦合系统中计算能带结构的两种方法，通过一维量子发射链在自由空间及与波导耦合情况对比，发现周期性边界条件结果更稳健，无限链方法有问题，且波导系统有非星形广义布里渊区等异常，解释了非厄米趋肤效应。
Dynamic Moiré-like pattern in non-Hermitian Wannier-Stark ladder system
该研究针对非厄米Wannier-Stark ladder系统，采用非厄米Floquet方法分析其在外场下的动力学行为，揭示了例外点分隔的两类动力学区域及非线性场下的动态类莫尔图案。
Fate of non-Hermitian free fermions with Wannier-Stark ladder
本文利用单粒子关联矩阵技术，研究了具有 Wannier-Stark 阶梯的非厄米自由费米子的纠缠行为，发现了独特的纠缠相和标度规律，揭示了非厄米趋肤效应与无序局域化相互作用产生的新奇物理现象。
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 measur…
Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
本研究将 Wannier-Stark 阶梯概念扩展至复数域，发现非厄米系统在实数 Bloch 频率下能级等距排列，支持带阻尼或增长速率的单粒子及双粒子 Bloch 振荡，并提出二聚化系统与二维晶格方案验证结果。
Circuit Design for a Star-shaped Spin-Qubit Processor via Algebraic Decomposition and Optimal Control
针对星形拓扑量子设备，提出基于代数分解与最优控制的电路设计算法，并在氮-空位中心平台上数值验证其可行性。
Dynamics of non-Hermitian Floquet Wannier-Stark system
在紧束缚近似框架下研究非厄米Floquet Wannier-Stark系统动力学，发现瞬时Hamiltonian能级等距且与时间及厄米性无关，共振时占据能级展宽并表现出$t^z$行为，实数与复数跳跃强度的动力学分别由指数$z=1$和$z=1/2$描述。
Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
在高维非厄运系统中，通过几何依赖的皮肤效应，实现了对束缚态几何结构的调控，使其从凹陷转变为凸起，并为实验操控束缚态提供了理论支持。
From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
本文研究了一维相互作用非厄米Stark模型，发现在周期边界条件下存在实复转变、拓扑相变和非厄米Stark多体局域化（MBL）转变，并通过能级统计和动力学演化揭示了这些相变特征。
Quasiparticle states in Dirac systems with complex impurity potentials are investigated. It is shown that an impurity site with loss leads to a nontrivial distribution of the local density of states (LDOS). While the real part of defect potential induces a well-pronounced peak in the density of states (DOS), the DOS is either weakly enhanced at small frequencies or even forms a peak at the zero frequency for a lattice in the case of non-Hermitian impurity. As for the spatial distribution of the LDOS, it is enhanced in the vicinity of impurity but shows a dip at a defect itself when the potenti…
Imposing chirality on a physical system engenders unconventional energy flow and responses, such as the Aharonov-Bohm effect and the topological quantum Hall phase for electrons in a symmetry-breaking magnetic field. Recently, great interest has arisen in combining that principle with broken Hermiticity to explore novel topological phases and applications. Here, we report unique phononic states formed when combining the controlled breaking of time-reversal symmetry with non-Hermitian dynamics, both induced through time-modulated radiation pressure forces in small nano-optomechanical networks. …
Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
本研究提出一种实空间重整化方法，统一分析厄米与非厄米模型的界面态，将其性质与参数流不动点拓扑关联，可直接用于设计目标特性界面，并推广至非线性场景且验证了有效性。
Critical properties in the non-Hermitian Aubry-Andre-Stark model
本文研究了具有准周期和Stark势的非厄米AAS模型的局域化转变临界性质，通过标度分析提取了新的临界指数，揭示了这些模型属于不同的普适类，并在临界区域重叠区建立了混合标度函数。
Non-Hermitian Stark Many-Body Localization
本文利用精确对角化技术研究带尾部曲率斯塔克势下的一维非互易相互作用硬核玻色子模型，发现谱实复转变临界点早于多体局域化相变，揭示了无无序非厄米系统中存在新颖的非MBL驱动的谱RC转变。
Krylov Complexity and Quantum Many-body Scars in Non-Hermitian Kinetically Constrained Models
本研究针对非厄米动力学约束模型，利用Arnoldi算法发现左、右本征态系综的克雷洛夫复杂度及本征态结构存在差异，揭示非厄米性对二者的不同影响，需分开处理非厄米动力学约束系统。
We describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the Hamiltonians $H=p^2+x^2(ix)^ν$ with $ν\in(-2,\infty)$ that are defined along the corresponding anti-Stokes lines. In particular, we reveal the intrinsic non-Hermiticity of $H$ for the cases that $ν$ is an even integer, so that $H=p^2\pm x^{2+ν}$, and give a proof of the discreteness of the spectrum of $H$ for all $ν\in(-2,\infty)$. Furthermore, we study the consequences of defining a square-well Hamilton…
Topological characterization of non-Hermitian band structures demands more than a straightforward generalization of the Hermitian cases. Even for one-dimensional tight-binding models with nonreciprocal hopping, the appearance of point gaps and the skin effect leads to the breakdown of the usual bulk-boundary correspondence. Luckily, the correspondence can be resurrected by introducing a winding number for the generalized Brillouin zone for systems with even number of bands and chiral symmetry. Here, we analyze the topological phases of a nonreciprocal hopping model on the stub lattice, where o…
We discuss the spectral properties of singular Schrödinger operators in three dimensions with the interaction supported by an equilateral star, finite or infinite. In the finite case the discrete spectrum is nonempty if the star arms are long enough. Our main result concerns spectral optimization: we show that the principal eigenvalue is uniquely maxi\-mized when the arms are arranged in one of the known five sharp configurations known as solutions of the closely related Thomson problem.
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency sp…
The fate of Wannier-Stark localization and skin effect in periodically driven non-Hermitian quasiperiodic lattices
本文研究周期驱动非厄米准周期晶格，发现慢调制电场产生多迁移率边新相，快驱动恢复无WS局域化，且驱动下趋肤效应出现并呈多分形。
Localization in microcavities revealed by phase-space non-Hermitian skin effect
该研究揭示了开放混沌螺旋形微腔中共振态临界线局域化的机制，将非厄米皮肤效应概念扩展至相空间，为相关物理现象提供了理论解释。
We consider the quantum state seen by an observer in the diamond-shaped region, which is a globally hyperbolic open submanifold of the Minkowski space-time. It is known from the operator-algebraic argument that the vacuum state of the quantum field transforming covariantly under the conformal group looks like a thermal state on the von Neumann algebra generated by the field operators on the diamond-shaped region of the Minkowski space-time. Here, we find, in the case of the free massless Hermitian scalar field in the 2-dimensional Minkowski space-time, that such a state can in fact be identifi…
We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex PT-invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES potentials. Further, by using anti-isospectral transformations, we obtain Hermitian as well as PT-invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender-Dunne polynomials.
We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with $l$-fold symmetry, ranging from quadrupole ($l=2$) to heptagon modes ($l=7$), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of …
We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.
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