球坐标动量空间下相对论Vlasov方程的数值算法

针对相对论Vlasov方程动量区间跨度大、难以计算的困难,将相对论Vlasov方程在球坐标动量空间中进行数值求解.对相对论Vlasov方程球坐标动量空间构造4阶非分裂守恒型数值格式.数值模拟相对论Landau阻尼问题并与解析理论进行比较,验证数值模型和算法的有效性.对激光等离子体相互作用进行初步模拟分析,表明通过采用球坐标下的动量空间,可在相对较少动量网格情形下,获得与粒子模拟可相互验证的结果.     

The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas

Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is botained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Resibois‘ method,we present the first principle formula of the relativistic heat conductivity of Coulumb electronic plasmas for low-order corrections.     

Mesoscopic superposition states in relativistic Landau levels

We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.     

Rearrangements of interacting Fermi liquids

The stability condition of the Landau Fermi liquid theory may be broken when the interaction between particles is strong enough. In this case, the ground state is reconstructed to have a particle distribution different from the Fermi-step function. For specific instances, one case with the vector boson exchange and another with the relativistic heavy-ion collision are taken into consideration. With the vector boson exchange, we find that the relative weak interaction strength can lead to the ground-state rearrangement as long as the fermion mass is large enough. It is found that the relativistic heavy-ion collision may also cause the ground-state rearrangement, affecting the statistics of the collision system.     

Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

Landau damping of longitudinal oscillation in ultra- relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.     

Broadening processes in GaAsδ-doped quantum wire superlattices

We use both Quantum Hall and Shubnikov de Haas experiments at high magnetic field and low temperature to analyse broadening processes of Landau levels in a δ -doped 2D quantum well superlattice and a 1D quantum wire superlattice generated from the first one by controlled dislocation slips. We deduce first the origin of the broadening from the damping factor in the Shubnikov de Haas curves in various configurations of the magnetic field and the measured current for both kinds of superlattice. Then, we write a general formula for the resistivity in the Quantum Hall effect introducing a dephasing factor we link to the process of localization.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

扇形多注强流相对论电子束的产生与传输研究

多注相对论速调管相对于常规相对论速调管, 每注电子束具有更低的导流系数和更低的空间电荷力, 却具有更高的束波转换效率. 本文基于这方面的需求, 通过三维软件模拟与实验研究了扇形多注强流相对论电子束的产生与传输. 通过建立电子枪的三维模型, 分析了阴极端面静电场的分布及其对电子束产生的影响; 通过粒子模拟获得了发射束流, 然后通过粒子跟踪仿真, 得到了电子束在空心漂移管和多扇形孔漂移管中传输的束斑图, 并对其进行了理论分析与解释. 模拟和实验结果表明, 电子束在空心漂移管传输过程中不仅绕束自身中心旋转, 还绕系统的中心旋转, 通过旋转多扇形孔漂移管实现对中的方法可提高传输效率.     

Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field

We show that the recently discovered double-valley splitting of the Landau levels in the quantum Hall effect in graphene can be explained as the perturbative orbital interaction of intravalley and intervalley microscopic orbital currents with a magnetic field. This effect is facilitated by the translationally noninvariant terms that correspond to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac fermions in quantum electrodynamics. We discuss recent data in view of these findings.     

Basic Aspect of Relativistic Rotation: Franklin Rotation of a Sphere

We give a relativistic treatment to the dynamics of spherical bodies rotating at very high speed. It is found that most of the mass of a homogeneous spherical quark with Franklin rotation is due to the relativistic increase of the mass.     

Landau levels for relativistic particles: Einstein–Brillouin–Keller quantization approach

The effects of a transverse magnetic field on relativistic particles in two dimensions are treated by using the semiclassical quantization rules and the role played by the spin is emphasized. The Landau levels? energies are analyzed by focusing on the square-root dependence on level index obtained for relativistic spinless particles. This result will be compared to the energies calculated for relativistic particles with spin that are governed by the Dirac equation in relativistic quantum mechanics. Then relativistic massless fermions are discussed. The approach provides a conceptual and intuitive introduction to the grounds of quantum Hall effect in carbon based nanostructures.     

On the interaction of the Dirac oscillator with the Aharonov–Casher system in topological defect backgrounds

In this paper, we study the influence of the Aharonov–Casher effect [Y. Aharonov, A. Casher, Phys. Rev. Lett. 53 (1984) 319] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov–Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.     

Giant monopole and quadrupole states in the relativistic σ-ω model

Giant monopole and quadrupole states in the relativistic σ-ω model are studied with use of a local Lorentz boost and scaling method. In assuming nuclear matter, those excitation energies are expressed in a simple way in terms of the relativistic Landau parameters, and the expressions are formally very similar to nonrelativistic ones. In the σ-ω model, however, the values of the Landau parameters themselves are dominated by relativistic effects. Unlike the restoring forces depending on the Landau parameters, the mass parameters of these states are little affected by relativity.     

Relativistic Landau‐He‐McKellar‐Wilkens quantization induced by noninertial effects

We show that the relativistic analogue of the Landau‐He‐McKellar‐Wilkens quantization can be achieved through the noninertial effects of the Fermi‐Walker reference frame without assuming the existence of a magnetic charge density and discuss the nonrelativistic limit of the energy levels. We also obtain the Dirac spinors for positive‐energy values parallel and antiparallel to the z axis of the spacetime and obtain the Gordon decomposition of the Dirac probability current J^μ.     

相对论简并电子气体的磁化

中子星内部的致密电子是高度简并的相对论气体, 其输运性质与中子星磁或热的观测现象密切相关, 被认为是中子星磁场的主要载体. 外磁场中电子的朗道能级是分立的且高度简并的, 与无外场时的能量差决定 了系统的磁化程度, 用量子统计的方法可计算理想相对论电子气体的磁化率. 结果表明弱场条件下的磁化率在数量级上接近白矮星的10^-3. 强磁场下的磁化呈现出类似在某些低温金属中出现的de Haas-van Alphen 震荡效应, 高次谐频的震荡幅度有可能超出临界磁化时的磁化率. 表明中子星内部有可能存在非稳定的磁化过程, 发生类似气液转化的一级相变过程, 出现两种磁化共存的稳定态或过冷磁化的亚稳态(若不同磁化态间存在表面能). 从亚稳态向稳定态的突然转化可能与磁星的辐射有关, 可以解释在磁星巨闪过程中观测到的额外辐射问题.     

UF_6分子价轨道相对论效应的理论电子动量谱学研究

用非相对论、标量相对论和二分量相对论三种不同的密度泛函方法对UF_6分子的电子结构进行了量子化学计算,并利用编写的程序计算出了三种方法下各个价轨道的电子动量谱,比较了三种方法计算的价轨道能级及动量分布的差异.结果表明,相对论效应不仅使UF_6的能级劈裂和移动,而且对部分价轨道电子动量分布有显著的影响.     

Novel electric field effects on Landau levels in graphene

A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.     

Quasi‐Relativistic Heat Equation via Lévy Stable Distributions: Exact Solutions

We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corresponding Cauchy (initial) problem using the operator formalism invoking one‐sided Lévy stable distributions. We note a natural appearance of Bessel polynomials which allow one to obtain closed form solutions for a number of initial conditions. The resulting diffusion is slower than the non‐relativistic one, although it still can be termed a normal one. Its detailed statistical characterization is presented in terms of exact evaluation of arbitrary moments and kurtosis and is compared with the non‐relativistic case.