分形体生长规律的透射光谱研究

本文初步讨论了不同体系中的分形体的生长规律,通过对不同分形体体系透射光谱的分析,发现透射光谱中新吸收带的位置与时间对数关系曲线大致由两条直线组成,这说明分形体的主要生长过程按速度大致可分为两个阶段。 关键词：     

分形体生长规律的透射光谱研究

本文初步讨论了不同体系中的分形体的生长规律, 通过对不同分形体体系透射光谱的分析, 发现透射光谱中新吸收带的位置与时间对数关系曲线大致由两条直线组成, 这说明分形体的主要生长过程按速度大致可分为两个阶段。 关键词：     

Fractal dynamics in the ionization of helium Rydberg atoms

We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory.By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization,we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons,and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy.We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons.Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field,and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms.It is shown that,besides the electric and magnetic fields,core scattering is a primary factor in the fractal dynamics.     

The fractal structure in the ionization dynamics of Rydberg lithium atoms in a static electric field

The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be considered as the promoted valence electrons escaping through the Stark saddle point into the ionization channels. The resulting escape spectrum of the ejected electrons demonstrates a remarkable irregular electron pulse train in time-dependence and a complicated nesting structure with respect to the initial launching angles. Based on the Poincaré} map and homoclinic tangle approach, the chaotic behaviour along with its corresponding fractal self-similar structure of the ionization spectra are analysed in detail. Our work is significant for understanding the quantum-classical correspondence.     

Magnetotransport in fractal network with loop sub-structures: Anisotropic effect and delocalization

We make an in-depth analysis of electronic transport and localization properties of non-interacting electrons in a Sierpinski gasket (SPG) fractal lattice in presence of magnetic field within a tight-binding framework. Unlike conventional symmetric systems, asymmetric SPG triangle leads to more conducting behavior, and thus delocalization of energy states, which we examine by calculating magnetic flux driven circular current and inverse participation ratio. The spectral peculiarity, that is the gapped nature of energy spectrum in fractal lattices, is clearly reflected from the variation of current with electron filling, yielding possibilities of getting filling dependent switching action. The effect of temperature is also discussed. Our analysis can be utilized to study magnetotransport properties in any other fractal lattices having loop sub-structures.     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001     

Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

We study the fractal rhythm in the ionization of Rydberg helium and lithium atoms in an electric field by using the semiclassical method. The fractal structures present a nested relationship layer by layer in the initial launch angles of the ionized electrons versus the escape time, which is defined as the rhythm attractor, and exhibit similar rhythm endings. The gradually enhanced chaotic regions of the escape time plots tend to broaden as the scaled energy increases. In addition,the fractal rhythm changes synchronously with the oscillations of the kinetic energy spectrum. We note that the intrinsic quality of the fractal rhythm is closely related to the kinetic energy distribution, that is, the inherent dynamic properties of the Hamiltonian equations have an impact on the fractal regularities. In addition, different ionizing closed trajectories exhibit iterate properties and the inherent beauty of symmetry. Our results and analysis can not only reveal new laws in the ionization of Rydberg atoms, but also promote the establishment of the dynamic mechanism of fractals.     

等离子体中相对论电子的同步曲率辐射特性研究

根据同步曲率辐射理论推导了在等离子体环境中,不同磁场条件下的相对论性电子的吸收系数和发射系数表达式，计算了电子的发射强度，并且在此基础上研究了同步曲率辐射机制的脉泽效应.研究了两种磁场位型，第一种是强度均匀但弯曲的磁场，第二种是偶极磁场，结果发现了一些偶极磁场下特有的辐射特性.考虑到在天体的环境下电子具有的不同的能谱分布，分别选用了三种典型的能谱分布(幂率分布，高斯分布，热分布)进行了研究，通过计算负吸收和脉泽放大效应在发射强度上的表现后， 发现在某些天体物理环境中，同步曲率辐射在等离子体中的确存在脉泽放大效应.这些研究结果对太阳系中行星外层辐射的研究和宇宙中的射电高亮温度等问题的研究可能提供有益的帮助. 关键词： 同步曲率辐射 负吸收 脉泽效应     

Exotic electron states and tunable magneto-transport in a fractal Aharonov–Bohm interferometer

A Sierpinski gasket fractal network model is studied in respect of its electronic spectrum and magneto-transport when each ‘arm’ of the gasket is replaced by a diamond shaped Aharonov–Bohm interferometer, threaded by a uniform magnetic flux. Within the framework of a tight binding model for non-interacting, spinless electrons and a real space renormalization group method we unravel a class of extended and localized electronic states. In particular, we demonstrate the existence of extreme localization of electronic states at a special finite set of energy eigenvalues, and an infinite set of energy eigenvalues where the localization gets ‘delayed’ in space (staggered localization). These eigenstates exhibit a multitude of localization areas. The two terminal transmission coefficient and its dependence on the magnetic flux threading each basic Aharonov–Bohm interferometer is studied in details. Sharp switch on–switch off effects that can be tuned by controlling the flux from outside, are discussed. Our results are analytically exact.     

Electromagnetic backscattering from one-dimensional drifting fractal sea surface I: Wave-current coupled model

To study the electromagnetic backscattering from a one-dimensional drifting fractal sea surface, a fractal sea surface wave-current model is derived, based on the mechanism of wave-current interactions. The numerical results show the effect of the ocean current on the wave. Wave amplitude decreases, wavelength and kurtosis of wave height increase, spectrum intensity decreases and shifts towards lower frequencies when the current occurs parallel to the direction of the ocean wave. By comparison, wave amplitude increases, wavelength and kurtosis of wave height decrease, spectrum intensity increases and shifts towards higher frequencies if the current is in the opposite direction to the direction of ocean wave. The wave-current interaction effect of the ocean current is much stronger than that of the nonlinear wave-wave interaction. The kurtosis of the nonlinear fractal ocean surface is larger than that of linear fractal ocean surface. The effect of the current on skewness of the probability distribution function is negligible. Therefore, the ocean wave spectrum is notably changed by the surface current and the change should be detectable in the electromagnetic backscattering signal.     

The intrinsical character of the electronic correlation in an electron gas

By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.     

The fractal energy measurement and the singularity energy spectrum analysis

The singularity exponent (SE) is the characteristic parameter of fractal and multifractal signals. Based on SE, the fractal dimension reflecting the global self-similar character, the instantaneous SE reflecting the local self-similar character, the multifractal spectrum (MFS) reflecting the distribution of SE, and the time-varying MFS reflecting pointwise multifractal spectrum were proposed. However, all the studies were based on the depiction of spatial or differentiability characters of fractal signals. Taking the SE as the independent dimension, this paper investigates the fractal energy measurement (FEM) and the singularity energy spectrum (SES) theory. Firstly, we study the energy measurement and the energy spectrum of a fractal signal in the singularity domain, propose the conception of FEM and SES of multifractal signals, and investigate the Hausdorff measure and the local direction angle of the fractal energy element. Then, we prove the compatibility between FEM and traditional energy, and point out that SES can be measured in the fractal space. Finally, we study the algorithm of SES under the condition of a continuous signal and a discrete signal, and give the approximation algorithm of the latter, and the estimations of FEM and SES of the Gaussian white noise, Fractal Brownian motion and the multifractal Brownian motion show the theoretical significance and application value of FEM and SES.     

锯齿型石墨纳米带叠层复合结的电子输运

基于紧束缚格林函数方法,研究了两半无限长锯齿型石墨纳米带叠层复合结的电子输运性质.结果表明,层间次近邻相互作用、叠层区长度及门电压对复合结的电子透射谱有重要调制作用.层间次近邻相互作用导致复合结的透射谱关于费米能呈现非对称性,与实验结果很好相符.低于费米能第一子能区内周期性出现透射系数为0和1的台阶,呈现全反射与透射现象.随散射结长度增加,透射系数在1内周期性振荡,呈现明显的量子干涉效应.在门电压调控下,低于费米能的透射系数出现了从1到0的转变,类似于开关效应.相关结果对基于石墨烯器件的设计与应用有指导意义.     

The time-singularity multifractal spectrum distribution

Although the multifractal singularity spectrum revealed the distribution of singularity exponent, it failed to consider the temporal information, therefore it is hard to describe the dynamic evolving process of non-stationary and nonlinear systems. In this paper, we aim for a multifractal analysis and propose a time-singularity multifractal spectrum distribution (TS-MFSD), which will hopefully reveal the spatial dynamic character of fractal systems. Similar to the Wigner–Ville time-frequency distribution, the time-delayed conjugation of fractal signals is selected as the windows function. Furthermore, the time-varying Holder exponent and the time-varying wavelet singularity exponent are deduced based on the instantaneous self-correlation fractal signal. The time-singularity exponent distribution i.e. TS-MFSD is proposed, which involves time-varying Hausdorff singularity spectrum distribution, time-varying large deviation multifractal spectrum and time-varying Legendre spectrum distribution, which exhibit the singularity exponent distribution of fractal signal at arbitrary time. Finally, we studied the algorithm of the TS-MFSD based on the wavelet transform module maxima method, analyzed and discussed the characteristic of TS-MFSD based on Devil Staircase signal, stochastic fractional motion and real sea clutter.     

Low-energy electron transmission in a partially unzipped zigzag nanotube

Based on the nearest-neighbor tight-binding approximation, we present exact analytical expressions for electron transmission in nanotube/ribbon junctions, generated by incomplete unzipping of zigzag nanotubes. By assuming one-dimer-line difference in the widths of the leads, it is demonstrated that such a contact exhibits zero backscattering of low-energy electrons entering from the graphene side of the junction. We also show that a zigzag nanotube section sandwiched between two armchair graphene ribbons is completely transparent for incident low-energy electrons. Possible application of the results to nanosensor engineering is also included.     

含氧空位锐钛矿TiO2光学性质的第一性原理研究

为了研究锐钛矿TiO2晶体中氧宅位对光学性质的影响,利用基于局域密度泛函理论框架下的广义梯度近似平面波超软赝势方法.用第一性原理对含氧空位锐钛矿TiO2晶体进行了结构优化处理.计算了完整的和含氧空位锐钛矿TiO2晶体的电子态密度、复数折射率、介电甬数及吸收光谱的偏振特性.二者比较发现,引入氧空位后,锐钛矿TiO2的电子结构发生了变化,电子总态密度的费米面进入了导带,引起了莫特相变;含氧空位的锐钛矿TiO2晶体的Ti 3d态大约在-6.097 eV处出现了新的劈裂峰值.两种模型的介电函数虚部、吸收光谱以及复折射率的实部,它们的峰值位置一一对应.说明它们之间存在着内在的联系,这些都与电子态密度分布直接相关.理论分析和计算发现二者的介电函数虚部和吸收光谱峰值位置移动是弛豫效应影响的结果,同时,峰值大小变化是电子跃迁的几率来决定的.晶体的各向异性是由晶体结构的对称性决定的.     

Über die charakteristischen Energieverluste bei Elektronenstreuung an Si-Spaltflächen

The energy spectrum of electrons scattered inelastically at cleavage surfaces of silicon and germanium into Bragg reflection spots differs from that obtained by transmission by low lying characteristic energy losses. The dependence of their intensity on the order of the diffraction spots, on the surface roughness, and on the angle near the diffraction spot shows that they are due to surface plasma oscillations. The transmission energy spectrum is mainly due to the excitation of volume plasma oscillations.     

Optical properties of metallic nanoshell composites: The effects of temperature and particle clustering

The optical properties of a metallic nanoshell composite are studied theoretically using different effective medium theories with particular focus on the effects of variation in temperature and particle clustering on these properties. One unique result from our modeling is the persistent manifestation of the single-particle resonances of the individual nanoshells which cannot be found in a composite of solid particles. In addition, we observe red-shifts in the composite plasmon modes, as well as damping in the dielectric function spectrum as the temperature increases. Furthermore, a much greater red-shift will occur when these nanoshells coalesce to form fractal clusters in the composite, with the value of this shift increasing with decrease in the fractal dimension or increase in the cluster size. We further calculate the transmission at normal incidence through such composite thin films as a demonstration of how these effects can be observed experimentally.