Observation of size-dependent boundary effects in non-Hermitian electric circuits

The non-Hermitian systems with the non-Hermitian skin effect(NHSE)are very sensitive to the imposed boundary conditions and lattice sizes,which lead to size-dependent non-Hermitian skin effects.Here,we report the experimental observation of NHSE with different boundary conditions and different lattice sizes in the unidirectional hopping model based on a circuit platform.The circuit admittance spectra and corresponding eigenstates are very sensitive to the presence of the boundary.Meanwhile,our experimental results show how the lattice sizes and boundary terms together affect the strength of NHSE.Therefore,our electric circuit provides a good platform to observe size-dependent boundary effects in non-Hermitian systems.

小学语文阅读教学策略研究

进入新时代,小学语文阅读教学策略也要与时俱进,不可一味因循守旧、墨守成规.从前,以教师的“灌输”为主,如今,当以引导学生主动学习为主.对于小学生而言,世界是新奇的,事物是新鲜而又难懂的.对事物的判断和认知都是从感官开始,继而在体验的不断深入以后,才有了进一步的感知,以及理解.基于小学生这方面的特点,笔者认为,在小学语文阅读教学策略中：第一,应当注重形象性和启发性.形象性,利于学生理解,引发“同理心”;启发性,利于学生主动思考和探究问题.第二,应当在一定程度上注重知识的积累,“死记硬背”也要有一定程度的运用,不能完全“弃之不用”.对于小学时期的学生而言,记忆力强和理解力弱,不但要注重孩子的当下,也要心系孩子的未来.因此“背记”仍然是为将来的深入学习与成长奠定较好基础的佳径.

State-Dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in Non-Hermitian Topological Systems with Generalized Inversion Symmetry

Breakdown of bulk-boundary correspondence in non-Hermitian(NH)topological systems with generalized inversion symmetries is a controversial issue.The non-Bloch topological invariants determine the existence of edge states,but fail to describe the number and distribution of defective edge states in non-Hermitian topological systems.The state-dependent topological invariants,instead of a global topological invariant,are developed to accurately characterize the bulk-boundary correspondence of the NH systems,which is very different from their Hermitian counterparts.At the same time,we obtain the accurate phase diagram of the one-dimensional non-Hermitian Su–Schrieffer–Heeger model with a generalized inversion symmetry from the state-dependent topological invariants.Therefore,these results will be helpful for understanding the exotic topological properties of various non-Hermitian systems.

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.

Emergent Quantum Dynamics of Vortex-Line under Linear Local Induction Approximation

Using the linear local induction approximation, we investigate the self-induced motion of a vortex-line that corresponds to the motion of a particle in quantum mechanics. Provided Kelvin waves, the effective Schr?dinger equation, physical quantity operators, and the corresponding path-integral formula can be obtained. In particular,the effective Planck constant defined by parameters of vortex-line motion shows the mathematical relation between the two fields. The vortexline–particle mapping may help in understanding particle motion in quantum mechanics.

Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

We study the two-dimensional weak-coupling Frohlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schrodinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.

Initial-Slip Term Effects on the Dissipation-Induced Transition of a Simple Harmonic Oscillator

We investigate the effects of the initial-slip term by studying the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. The general analytical expressions for the transition probabilities are obtained, then the special cases of transition probabilities ignoring the Brownian motion from the ground state to the first few excited states are discussed. It is found that the initial-slip term not only makes the forbidden transitions between states of different parity possible but also lifts the initial value of the transition probabilities.