From Dirac’s Aether to the Dirac Equation

In 1951, Dirac proposed a formalism for a Lorentz invariant Aether with a vacuum state that contains all possible velocity states at each space-time point. Dirac showed no explicit path from the Aether towards the Quantum Mechanics. In this paper, we demonstrate that Dirac’s proposed Aether can be described by a lattice of possible events in space-time built in the local Lorentz frame. The idealised case of single velocity state leads to the famous Dirac equation for a plane wave state and is compatible with quantum statistics. On the lattice, possible space-time events are connected by the Dirac spinors which provide the probability of observing an event. The inertial mass of a particle is shown to be equivalent to the density of possible events on the lattice. Variation of the lattice density of events modifies the metric and provides a space-time curvature leading to the Hilbert action associated with general relativity. In classical limit, the perturbation in the density of possible events of the Aether is proportional to the Newtonian gravitational potential.

紧Spin流形上Dirac-Laplace方程解的存在性

本研究利用对称形式的山路定理阐释了紧Spin流形上Dirac-Laplace方程解的存在性,改进了文献[2]中的条件,得到了Dirac-Laplace方程具有无穷多对不同的解,这为高阶Dirac方程解的存在性研究提供了重要的参考.

一种基于Dirac半金属的可调控极化偏转器件的仿真分析

本文提出了一种基于体Dirac半金属(Bulk Dirac Semimetal,BDS)的动态超材料结构极化偏转器.与传统的极化偏转器不同,该偏转器可以通过改变费米能级来动态控制偏振转换率和不对称传输.模拟结果表明,当BDS的费米能级调整为90 meV时,偏转器的偏振转换率在1.085~1.872 THz频率范围内都保持在90%以上(带宽为0.787 THz),在1.159 THz处偏振转换率达到峰值98%.该偏振转换器的不对称传输参数在1.229~1.831 THz大带宽范围内大于60%.本文还研究了偏振旋转角、椭圆度角、表面电流和电场分布情况以阐明该器件的极化转换特性和物理机制;通过施加栅极电压控制BDS费米能级,实现了对该极化偏转器的偏振转换率以及不对称传输的动态调谐.该极化偏转器的可调谐不对称传输特性,为基于动态不对称传输所设计的多路复用器、太赫兹二极管等设备的制造提供了新的思路.

含有Dirac位势的非线性S-P方程的约束极小元

该文研究了一类含有Dirac位势的非线性Schrödinger-Poisson方程的约束变分问题,在一定的参数和指标假设条件下,证明了约束极小元的存在性,推广了文献[2]中的相关结论.

具有手性边界条件的耦合Dirac系统

本文研究具有手性边界条件的Dirac系统解的存在性.通过在恰当的分数阶索伯列夫乘积空间上建立解析框架,给出了具有超二次增长的非线性项的Dirac系统解的存在性,把GONG和LU(2017)研究的结果推广到手性边界条件下的情形.

共形扭化Dirac算子与非交换留数

考虑了一类共形扭化Dirac算子,给出了其Lichnerowicz公式.利用Laplace算子的局部表示,在法坐标系下计算出了无边流形与共形扭化Dirac算子相关的非交换留数.

一类具有复权函数和两个不连续点的Dirac算子的逆问题

本文考虑了一类具有转移条件和复值权函数的Dirac算子的逆问题,采用了谱映射的方法得到了具有两个不连续点的Dirac算子的势函数在整个区间能被两组谱或Weyl函数唯一确定。

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Magnetic Topological Dirac Semimetal Transition Driven by SOC in EuMg_(2)Bi_(2)

Magnetic topological semimetals have been at the forefront of condensed matter physics due to their ability to exhibit exotic transport phenomena.Investigating the interplay between magnetic and topological orders in systems with broken time-reversal symmetry is crucial for realizing non-trivial quantum effects.We delve into the electronic structure of the rare-earth-based antiferromagnetic Dirac semimetal EuMg_(2)Bi_(2) using first-principles calculations and angle-resolved photoemission spectroscopy.Our calculations reveal that the spin-orbit coupling(SOC)in EuMg_(2)Bi_(2) prompts an insulator to topological semimetal transition,with the Dirac bands protected by crystal symmetries.The linearly dispersive states near the Fermi level,primarily originating from Bi 6p orbitals,are observed on both the(001)and(100)surfaces,confirming that EuMg_(2)Bi_(2) is a three-dimensional topological Dirac semimetal.This research offers pivotal insights into the interplay between magnetism,SOC and topological phase transitions in spintronics applications.

Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field

We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.

Coexistence of Dirac and Weyl points in non-centrosymmetric semimetal NbIrTe_(4)

Using angle-resolved photoemission spectroscopy and density functional theory calculations methods,we investigate the electronic structures and topological properties of ternary tellurides NbIrTe_(4),a candidate for type-II Weyl semimetal.We demonstrate the presence of several Fermi arcs connecting their corresponding Weyl points on both termination surfaces of the topological material.Our analysis reveals the existence of Dirac points,in addition to Weyl points,giving both theoretical and experimental evidences of the coexistence of Dirac and Weyl points in a single material.These findings not only confirm NbIrTe_(4) as a unique topological semimetal but also open avenues for exploring novel electronic devices based on its coexisting Dirac and Weyl fermions.

Single pair of charge-2 Dirac and charge-2Weyl phonons in GeO_(2)

The presence of a pair of Weyl and Dirac points(WP-DP)in topological semimetal states is intriguing and sought after due to the effects associated with chiral topological charges.However,identifying these states in real materials poses a significant challenge.In this study,by means of first-principles calculations we predict the coexistence of charge-2 Dirac and charge-2 Weyl phonons at high-symmetry points within a noncentrosymmetric P4_(1)2_(1)2 space group.Furthermore,we propose GeO_(2)as an ideal candidate for realizing these states.Notably,we observe two distinct surface arcs that connect the Dirac and Weyl points across the entire Brillouin zone,which could facilitate their detection in future experimental investigations.This study not only presents a tangible material for experimentalists to explore the topological properties of WP-DP states but also opens up new avenues in the quest for ideal platforms to study chiral particles.

Controllable optical bistability in a Fabry-Pérot cavity with a nonlinear three-dimensional Dirac semimetal

Optical bistability(OB)is capable of rapidly and reversibly transforming a parameter of an optical signal from one state to another,and homologous nonlinear optical bistable devices are core components of high-speed all-optical communication and all-optical networks.In this paper,we theoretically investigated the controllable OB from a Fabry-Pérot(FP)cavity with a nonlinear three-dimensional Dirac semimetal(3D DSM)in the terahertz band.The OB stems from the third-order nonlinear bulk conductivity of the 3D DSM and the resonance mode has a positive effect on the generation of OB.This FP cavity structure is able to tune the OB because the transmittance and the reflectance can be modulated by the Fermi energy of the 3D DSM.We believe that this FP cavity configuration could provide a reference concept for realizing tunable bistable devices.

Equivalence of the Aharonov-Bohm and Dirac Monopole Potentials

The Aharonov-Bohm effect (experimentally verified) constitutes an undubitable proof of the non local nature of quantum mechanics and of the gauge character of the electromagnetic interaction. On the other hand, the existence of a Dirac monopole (not yet experimentally confirmed) leads to the quantization of the electric charge. Both phenomena can be mathematically described in the context of fiber bundle theory. Using this approach, we briefly review the mutual determination of the corresponding connections ωA−B, ωDand potentials AA−B±, AD±. This mathematical result gives an additional theoretical support to present day active search of the magnetic charge.

初值含Dirac函数的一个简化趋化性模型的Riemann问题

利用相平面分析法和广义Rankine-Hugoniot条件讨论一个含Dirac初值的简化趋化性模型的Riemann问题.根据初值q±,q0和0之间的大小关系,将问题分为5种情形讨论,并构造性地得到了该问题的全局解.最后,利用数值模拟验证理论结果的正确性.

紧Spin流形上具有凹凸非线性项的Dirac方程解的存在性

利用变分方法研究了紧Spin流形上具有凹凸非线性项的Dirac方程解的存在性,得到了2列具有趋于零的负能量序列解和无界能量序列解.

渐近线性Dirac方程的相对Morse指标及其多解性

该文主要研究Dirac方程周期解的存在性和多重性.通过引入相对Morse指标对相应的线性Dirac方程进行分类,并给出解存在的扭转性条件.

Photonic Dirac cone and topological transition in a moving dielectric slab

The moving media theory is applied to a photonic confined structure which is a continuous dielectric slab waveguide with the uniaxial anisotropy and without the discrete translational symmetry.The moving effect not only brings about non-reciprocity to the whole photonic band structure in the co-moving and counter-moving directions,but also leads to the topological transition of local degenerate points within the band diagram.We demonstrate through calculation that the type-ⅡDirac point can be turned into type-ⅠDirac point when the uniaxial slab is moving over certain speed.Our results provide a new approach to regulate the topology of degeneracy for two-dimensional photonic bands in the continuous translational symmetry condition.

Chiral Dirac Fermion in a Collinear Antiferromagnet

In a Dirac semimetal, the massless Dirac fermion has zero chirality, leading to surface states connected adiabatically to a topologically trivial surface state as well as vanishing anomalous Hall effect. Recently, it is predicted that in the nonrelativistic limit of certain collinear antiferromagnets, there exists a type of chiral“Dirac-like” fermion, whose dispersion manifests four-fold degenerate crossing points formed by spin-degenerate linear bands, with topologically protected Fermi arcs. Such an unconventional chiral fermion, protected by a hidden SU(2) symmetry in the hierarchy of an enhanced crystallographic group, namely spin space group, is not experimentally verified yet. Here, by angle-resolved photoemission spectroscopy measurements, we reveal the surface origin of the electron pocket at the Fermi surface in collinear antiferromagnet CoNb3S6. Combining with neutron diffraction and first-principles calculations, we suggest a multidomain collinear antiferromagnetic configuration, rendering the the existence of the Fermi-arc surface states induced by chiral Dirac-like fermions.Our work provides spectral evidence of the chiral Dirac-like fermion caused by particular spin symmetry in CoNb_(3)S_(6), paving an avenue for exploring new emergent phenomena in antiferromagnets with unconventional quasiparticle excitations.