Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how to analytically solve the systems under some specific boundary conditions.Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters,we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations,which give the specific boundary conditions.Our analytical results show that the wave functions take simple forms and are independent of hopping range,while the eigenvalue spectra display rich model-dependent structures.Particularly,we find the existence of a special point coined as pseudo-periodic boundary condition,for which the eigenvalues are the same as those of the periodical system when the hopping parameters fulfill certain conditions,whereas the eigenstates display the non-Hermitian skin effect.     

Analytical study of surface states caused by the edge decoration

Analytical studies of the effect of edge decoration on the energy spectrum of semi-infinite one-dimensional (1D) model and zigzag edged graphene (ZEG) are presented by means of transfer matrix method, in the frame of which the conditions for the existence of edge states are determined. For 1D model, the zero-energy surface state occurs regardless of whether the decorations exist or not, while the non-zero-energy surface states can be induced and manipulated through adjusting the edge decoration. On the other hand, the case for the semi-infinite ZEG model with nearest-neighbour interaction is discussed in the analogous way. The non-zero-energy surface states can be induced by the edge decoration and moreover, the ratio between the edge hopping and the bulk hopping amplitudes should be within a certain threshold.     

一维长程关联无序系统中的电子态

利用傅里叶滤波法在一维Anderson无序系统中产生了具有幂律谱密度公式s(q)∝q^-p形式的长程关联随机能量序列，并利用传输矩阵方法计算了系统中引入了长程关联后的局域长度，同时应用负本征值理论对系统中的电子态密度进行了分析，并分别把计算结果与系统中不具有长程关联时的局域长度与电子态密度进行了比较.结果表明，长程幂律关联的引入对电子态的性质产生了很大的影响，当关联指数p≥2.0时，在系统能带中心范围内发生了部分局域态向退局域态的转变，而同时电子态密度也发生了很大的变化，出现了六个范霍夫奇点，系统的能带范围也相应地得到展宽. 关键词： 无序系统 长程关联 局域长度 电子态密度     

Nonequilibrium phase transitions in stochastic lattice systems: Influence of the hopping rates

Two-dimensional lattice-gas models with attractive interactions and particle-conserving hopping dynamics under the influence of a very large external electric field E along a principal axis are studied in the case of different ratios between the jump rates in the field direction and perpendicular to it using different transition probabilities. We investigate the dependence of the non-equilibrium steady-state properties on the transition mechanism. We find self-similarity with respect to (T, ) and a coexistence curve critical exponent which, for small, seems independent of. There is some evidence that this exponent might be halfway between the equilibrium mean field and Onsager's values. A crossover toward mean-field behavior for large seems also identified.Partially supported by the US-Spanish Cooperative Research Program, Grant CCB-8402025.     

磁铁边缘场对注入束流的影响

在兰州重离子加速器冷却储存环工程(HIRFL–CSR)实验环的注入设计过程中,通过对束流在侧面边缘场作用下运动的反向数值跟踪,得到注入束流通过二极磁铁和四极透镜边缘场的传输矩阵,并同理想场对束流的作用进行了比较.通过改变注入束流中心轨道及对磁铁的重新设计,将磁铁边缘场对注入束流的影响减小到可以控制的范围.     

Theoretical study of W-shaped optical fiber with a depression in core center by applying analytical transfer matrix method

Analytical transfer matrix method (ATMM) is a method for calculating the propagation constant in weakly guiding optical fiber. By using ATMM, the optical fiber with a depression in the index profile center and a valley in the cladding layer is analyzed. Compared with Wentzel-Kramers-Brillouin (WKB) method, the simulation result of differential mode delay (DMD) by using ATMM fits well with the experimental results obtained by Takahashi. Based on ATMM, by increasing the depth of central depression in a W-shaped index fiber, the improvement of DMD is also discussed.     

Topological and Nontopological Edge States Induced by Qubit-Assisted Coupling Potentials

In the usual Su–Schrieffer–Heeger (SSH) chain, the topology of the energy spectrum is divided into two categories in different parameter regions. Here, the topological and nontopological edge states induced by qubit-assisted coupling potentials in circuit quantum electrodynamics (QED) lattice modeled as a SSH chain are studied. It is found that, when the coupling potential added on only one end of the system raises to a certain extent, the strong coupling potential will induce a new topologically nontrivial phase accompanied by the appearance of a nontopological edge state, and the novel phase transition leads to the inversion of odd–even effect directly. Furthermore, the topological phase transitions when two unbalanced coupling potentials are injected into both ends of the circuit QED lattice are studied, and it is found that the system exhibits three distinguishing phases with multiple flips of energy bands. These phases are significantly different from the previous phase induced via unilateral coupling potential due to the existence of a pair of nontopological edge states. The scheme provides a feasible and visible method to induce different topological and nontopological edge states through controlling the qubit-assisted coupling potentials in circuit QED lattice both in experiment and theory.     

Change-over switch for quantum states transfer with topological channels in a circuit-QED lattice

We propose schemes to realize robust quantum states transfer between distant resonators using the topological edge states of a one-dimensional circuit quantum electrodynamics(QED)lattice.Analyses show that the distribution of edge states can be regulated accordingly with the on-site defects added on the resonators.And we can achieve different types of quantum state transfer without adjusting the number of lattices.Numerical simulations demonstrate that the on-site defects can be used as a change-over switch for high-fidelity single-qubit and two-qubit quantum states transfer.This work provides a viable prospect for flexible quantum state transfer in solid-state topological quantum system.     

Topological photonic states in gyromagnetic photonic crystals: Physics,properties, and applications

Topological photonic states (TPSs) as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects, disorders and metallic obstacles. Gyromagnetic photonic crystal (GPC) is the first artificial microstructure to implement TPSs, and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties, transport phenomena, and advanced applications. Herein, we present a brief review of the fundamental physics, novel properties, and practical applications of TPSs based on GPCs. We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices, antichiral one-way edge states in cross magnetized GPCs, and robust one-way bulk states in heterogeneously magnetized GPCs. Then, we discuss the strongly coupling effect between two co-propagating (or counter-propagating) TPSs and the resulting physical phenomena and device applications. Finally, we analyze the key issues and prospect the future development trends for TPSs in GPCs. The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.     

氩原子共振增强多光子电离谱--奇对称性里德堡态

利用脉冲放电产生氩原子亚稳态4s2[3/2]°2和4s′2[1/2]°0,在610～670nm波长范围内,利用共振增强多光子电离和飞行时间质谱技术得到氩原子(2+1)REMPI谱.光谱分析表明所有谱线来源于氩原子4s2[3/2]2和4s′2[1/2]°0两个亚稳态向16个奇对称性里德堡态双光子跃迁,并标识所有谱线.同时首次在实验上观察到一个长序列的3p54s′2[1/2]°0→3p5nd2[1/2]°1(n=8～31)双光子跃迁.在实验技术上,提供了一种研究惰性气体原予以及其它原子高里德堡态和自电离态的新方法.     

Mode hopping in single-mode microchip Nd：YAG lasers induced by optical feedback

The mode hopping phenomenon induced by optical feedback in single-mode microchip Nd：YAG lasers is presented. With optical feedback, mode hopping strongly depends on two factors： the ratio of external cavity length to intra-cavity length, and initial gains of the two hopping modes, When external cavity length equals an integral multiple of intracavity length, there is almost no mode hopping. However, if the external cavity length does not equal an integral multiple of intra-cavity length, mode hopping occurs. The ratio of external cavity length to intra-cavity length determines the position of two-mode hopping, The initial gains of the two hopping modes determine the corresponding peak values and oscillating periods of them in the intensity modulation curves.     

Intensity modulation and multi modes hopping induced by phase change in external cavity Nd:YAG lasers

Intensity modulation and multi modes hopping in Nd:YAG lasers subjected to optical feedback have been studied experimentally and theoretically. Their dependence on the external-cavity-phase has been studied. The results are compared with the predictions of the model of threshold gain modulation. As the initial length of external cavity is changed the number of hopping modes also changes.     

Identifying stochastic basin hopping by partitioning with graph modularity

It has been known that noise in a stochastically perturbed dynamical system can destroy what was the original zero-noise case barriers in the phase space (pseudobarrier). Noise can cause the basin hopping. We use the Frobenius-Perron operator and its finite rank approximation by the Ulam-Galerkin method to study transport mechanism of a noisy map. In order to identify the regions of high transport activity in the phase space and to determine flux across the pseudobarriers, we adapt a new graph theoretical method which was developed to detect active pseudobarriers in the original phase space of the stochastic dynamic. Previous methods to identify basins and basin barriers require a priori knowledge of a mathematical model of the system, and hence cannot be applied to observed time series data of which a mathematical model is not known. Here we describe a novel graph method based on optimization of the modularity measure of a network and introduce its application for determining pseudobarriers in the phase space of a multi-stable system only known through observed data.     

Energy eigenvalues from an analytical transfer matrix method

A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.     

Excited states of Ne isoelectronic ions: SAC-CI study

Excited states of the s, p, and d symmetries up to principal quantum number n = 4 are studied for the first eight members of Ne isoelectronic sequence (Ne to Cl⁷⁺) by the SAC-CI (symmetry-adapted-cluster configuration-interaction) method. The valence STO basis sets of Clementi et al. and the optimized excited STO are used by the STO-6G expansion method. The calculated transition energies agree well with the experimental values wherever available. Received 26 July 2000 and Received in final form 14 September 2000     

激发态之间的电离与复合过程对类氖锗19.6nm X射线激光增益系数的影响

考察了激发态之间的电离与复合过程对等离子体状态的影响,并对其原因进行了细致的分析,分别考察了对1.0ns,100ps和5ps激光驱动的类氖锗19.6nm Ｘ射线激光增益系数的影响.研究表明,对于5ps激光驱动的瞬态机理X射线激光来讲,因增益区处在高密度区,所以,激发态之间的电离与复合过程对X射线激光将不可以忽略.对于1.0ns和100ps激光驱动的亚稳态机理X射线激光来讲,在电子密度小于等于5×10²⁰cm^－3的区域,忽略激发态之间的电离与复合使增益的时间半高全 关键词： X射线激光 矩阵分块法 类氖锗 双电子激发态     

Density of states and extent of wave function: two crucial factors for small polaron hopping conductivity in 1D

Abstract

We introduce a theoretical model to scrutinize the conductivity of small polarons in 1D disordered systems, focusing on two crucial – as will be demonstrated – factors: the density of states and the spatial extent of the electronic wave function. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task, we combine analytical work with numerical calculations.