Majorana表象下的纠缠动力学

借助在Majorana表象下提出的纠缠度定义, 研究了对称双阱中两个玻色原子组成的系统的纠缠动力学. 得到了系统的任意态在Majorana 表象下的表示, 并考察了原子间相互作用及系统初始状态对纠缠度动力学的影响. 发现原子间相互作用会决定纠缠度振荡的频率, 而纠缠度振荡的幅度对系统的初态很敏感.     

Polarization effects in the Majorana representation

Maxwell’s equations in the Majorana form are extended to the case of a orthogonal curvilinear system of coordinates. The optical Magnus effect is considered as an example. The results obtained are extended to massless spin particles with half-integer spins.     

非线性两模玻色子系统的Majorana表象

利用Majorana表象,从平均场模型和二次量子化模型两方面研究了非线性双模玻色子系统的动力学问题.得到了Majorana点在球面上的运动方程,分析了平均场模型和二次量子化模型之间的区别及其在Majorana点运动方程中的体现.研究了二次量子化模型中量子态在少体和多体情况下的动力学演化及其与平均场量子态的区别和联系.以平均场模型和二次量子化模型量子态之间的保真度和Majorana点之间的关联为手段,讨论了在不同玻色子间相互作用强度、不同玻色子数下量子态的演化及相应的自囚禁效应.     

Inverse optical magnus effect in the Majorana representation

An equation describing the effect of additional bending during photon motion along a twisted path is obtained from Maxwell’s equations in the Majorana representation. The generalized Rytov law in an arbitrary curvilinear system of coordinates forms the basis for the effect. The effect considered is inverse to the optical Magnus effect.     

Maxwell’s equations in the Majorana representation in a locally isotropic chiral medium

Maxwell’s equations in the Majorana representation are generalized to the case of a chiral medium. A relation between the dynamic variables and the parameters of a chiral medium is found. An expression for the current density 4-vector is obtained for the medium under consideration.     

Effective potential for emergent Majorana fermions in superconductor systems

Majorana fermions cannot be found in nature as a free fundamental particle. Nevertheless, in condensed matter systems, they can emerge as a collective excitation. In this work, using functional integration techniques, we calculated the effective potential for emergent Majorana fermions in the Kitaev chain. In this case, we have shown the behavior of the superconductor parameter as a function of temperature. Furthermore, we considered surface-induced superconductivity in a Topological Insulator and calculated the effective potential for emergent Majorana fermions in this system. In the case of an s-wave superconductor, we obtained a gap equation equivalent to that one appearing in a quasi-two-dimensional Dirac electronic system, a candidate to explain high-Tc superconductivity. Finally, for the p-wave superconductor, we have obtained a critical value of the electron-electron interaction in the surface of the Topological Insulator, determining the existence or not of induced superconductivity, a remarkable result to guide experiments.     

Majorana stellar representation for mixed-spin (s, 1/2) systems

By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s?1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s?1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s?1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.     

Maxwell’s equations in the Majorana representation in chiral and gyrotropic media

Maxwell’s equations in the Majorana representation are generalized to the case of chiral and gyrotropic media. A relation between the dynamic variables and the parameters of chiral and gyrotropic media is found. An expression for the current density 4-vector is obtained for the media considered.     

Optical potential discrete variable representation method in the adiabatic representation

The optical potential discrete variable representation method (OP-DVR) has been applied recently to calculate resonances in the framework of the diabatic representation [J. Chem. Phys. 101, 7580 (1994)]. This method is based on the conjoint use of the discrete variable representation (DVR) method and the properties of a complex absorbing potential (CAP). The OP-DVR method is the DVR version of the CAP stabilization method initially proposed by Jolicard and Austin [Chem. Phys. Lett. 121, 106 (1985)]. In the present study, we show that this efficient and accurate method can also be applied within the adiabatic representation since it allows one to overcome in a simple way, numerical difficulties associated with the first derivative operator which appears in the expression of non adiabatic couplings. Within the OP-DVR method, the choice of the representation (diabatic or adiabatic) is governed by physical arguments and by the fact that the potentials and the couplings are known in one or the other of these two representations. In the case where the potentials and the couplings are obtained in the adiabatic representation, we show in this paper that the transformation into the diabatic framework is not necessary. We demonstrate that the discrete variable representation can be a simple and an efficient way to deal with the adiabatic representation. Received: 30 April 1998 / Revised: 29 September 1998 /Accepted: 21 October 1998     

Majorana Representation for a Composite System

International Journal of Theoretical Physics - The Majorana representation, which provides an intuitive way to represent the quantum state by stars on the Bloch sphere, has drawn considerable...     

An analytic representation for the potential of a uniform elliptic cone

In view of the fact that various gravitating and charged bodies may have singular points on their surface, the problem of the effect of these singularities in the mass distribution on the behavior of potential arises. The analytic representation for gravitational and electrostatic potentials of a uniform elliptic cone in terms of ordinary integrals is derived. Generally, these integrals are somewhat more complicated than the elliptic ones; however, they reduce to elementary functions in the case of a circular cone. The arbitrariness in the way of truncating a cone manifests itself in the possibility of adding various harmonic polynomials. However, the singularity of potential in the vicinity of the vertex of a cone is of an objective and unique character.     

Introduction to Majorana masses

We present a pedogogical review of Majorana masses and Majorana's theory of two-component massive fermions. We discuss the difference between Majorana and Dirac masses and show that Majorana masses are formion-number violating. We discuss the connection between Majorana and, Weyl spinors and show that the massive Majorana and Weyl field theories are equivalent. We study the second quantization of the massive Weyl theory in detail.     

A new representation of the heavy ion Coulomb potential

The Coulomb potential between two heavy ions at their interpretation condition has been represented in terms of two point charges with reduced effective charge, dependent on overlap volume. This representation enables visualization of the dynamic development of the deformations of the colliding nuclei as a function of the degree of overlap. The potential has been compared with well known potentials for heavy-ion collisions. This Coulomb potential gave good agreement in reproducing excitation functions for fusion for a large number of heavy-ion systems.     

Open multistate Majorana model

The Majorana model in the presence of dissipation and dephasing is considered. First, it is proven that increasing the Hilbert space dimension the system becomes more and more fragile to quantum noise, whether dephasing or dissipation are mainly present. Second, it is shown that, contrary to its ideal counterpart, the dynamics related to the open Majorana model cannot be considered as the combined dynamics of a set of independent spin-1/2 models.     

环状非有心球谐振子势场赝自旋对称性的三对角化表示

提出一个包含非有心电耦极矩势的环状谐振子模型,在能够负载波动算子三对角化矩阵表示的完全平方可积L2空间讨论了这一势场的赝自旋对称性．利用三对角化矩阵方案,给出了波函数角向分量和径向分量展开系数满足的三项递推关系式．角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示,由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱．并以Descartes多项式的符号法则讨论了能量方程的代数结构．     

Covariant Majorana Formulation of Electrodynamics

We construct an explicit covariant Majorana formulation of Maxwell electromagnetism which does not make use of vector 4-potential. This allows us to write a Dirac equation for the photon containing all the known properties of it. In particular, the spin and (intrinsic) boost matrices are derived and the helicity properties of the photon are studied.