Clifford代数的spinor表示空间

讨论了Clifford代数的结构 ,证明Clifford代数的pinor或spinor空间都可以表示为其子空间 ,且都可以由一个元素生成 .选取不可约表示空间的基 ,具体建立了Clifford代数与矩阵代数之间的同构 .

Clifford代数的Spinor表示空间

讨论了Clifford代数的结构 ,证明Clifford代数的Pinor或Spinor空间都可以表示为它们的子空间 ,且都可以由一个元素生成 选取不可约表示空间的基 。

PLANNING MOTION TRACE OF ROBOT BY SPINOR METHOD

The spinors applied to describe position and attitude of robot are studied. In dual spaces, the terminal trace of robot is planned through the mapping point, of attitude spinors. As a handy method directly perceived through the sense, the spinor method directly converges tracking error in the planning. It promotes the dynamic accuracy of trace operation. It is also suitable to the exerciser with redundant freedom.

Dynamics of spinor Bose–Einstein condensate subject to dissipation

We investigate the internal dynamics of the spinor Bose-Einstein condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along a specific orbital in the phase space of （no, O） and display three kinds of dynamical properties including Josephson-like oscil- lation, self-trapping-like oscillation, and ＇running phase＇. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-（-1） dissipate at different rates, the magnetization m will not conserve and the system transits between different dynamical regions. The dynamical properties can be exhibited in the ohase soace of （nn, θ, m）.

Coherent spin dynamics in spin-imbalanced ferromagnetic spinor condensates

We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate（BEC） in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain structure, a semiclassical theory that captures the essential dynamics of the system is presented, and the coherent spin mixing dynamics can be understood in terms of oscillation in the phase space diagram. Using the phase diagram analysis method, we identify new phases, including the π phase oscillation and the running phase for the spin-imbalanced ferromagnetic spinor BEC.

AFFINE SPINOR DECOMPOSITION IN THREE-DIMENSIONAL AFFINE GEOMETRY

Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.

Quantized vortices in spinor Bose–Einstein condensates with time–space modulated interactions and stability analysis

The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex solutions of the spinor BECs with spatiotemporally modulated interactions are worked out by similarity transformation. Theoretical analysis and numerical simulation of vortex states are demonstrated. Stable vortex states are obtained by adjusting the frequency of the external potential and the spatiotemporally modulated interaction.

Spinor F=1 Bose-Einstein condensates loaded in two types of radially-periodic potentials with spin-orbit coupling

We consider two-dimensional spinor F=1 Bose-Einstein condensates in two types of radially-periodic potentials with spin-orbit coupling,i.e.,spin-independent and spin-dependent radially-periodic potentials.For the Bose-Einstein condensates in a spin-independent radially-periodic potential,the density of each component exhibits the periodic density modulation along the azimuthal direction,which realizes the necklacelike state in the ferromagnetic Bose-Einstein condensates.As the spin-exchange interaction increases,the necklacelike state gradually transition to the plane wave phase for the antiferromagnetic Bose-Einstein condensates with larger spin-orbit coupling.The competition of the spin-dependent radially-periodic potential,spin-orbit coupling,and spin-exchange interaction gives rise to the exotic ground-state phases when the Bose-Einstein condensates in a spin-dependent radially-periodic potential.

APPLICATION OF SPINOR METHOD TO THE DYNAMIC ANALYSIS OF ROBOT

A method known as spinor method is applied to the study of dynamic model of robot.It merges velocity and angular velocity.Force and moments into an organic whole by their internal relation, and mates Newton-Euler method more concise and efficient.A reference system is formed with respect to the mass center of the arms of robot, which simplifies the calculation of inertial lensor and mass center acceleration.And further reduces work load in calculation, and thus ensures a fast real-timecalculation.

Cluster mean-field study of spinor Bose-Hubbard ladder:Ground-state phase diagram and many-body population dynamics

We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose-Hubbard ladder(BHL).For unbiased BHL,we find superfluid(SF)phase and integer filling Mott insulator(Int MI)phase.For biased BHL,in addition to the SF and Int MI phases,there appears half-integer filling Mott insulator(HInt MI)phase.The phase transition between the SF and Int MI phases can be first order at a part of phase boundaries,while the phase transition between the SF and HInt MI phases is always second order.By tuning the bias energy,we report on the change of the nature of SF-MI phase transitions.Furthermore,we study the effect of the spin-dependent interaction on the many-body population dynamics.The spin-dependent interaction can lead to rich dynamical behaviors,but does not influence the particle transfer efficiency.Our results indicate a way to tune the nature of the SF-MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.

Spin current in a spinor Bose–Einstein condensate induced by a gradient magnetic field

We develop a research of spin currents in a^(23)Na spinor Bose–Einstein condensate(BEC)by applying a magnetic field gradient.The spin current is successfully induced by the spin-dependent force arising from the magnetic field gradient.The dynamics of the spin components under the magnetic force is investigated.The study is promising to be extended to produce a longer spin-coherence and to enhance the sensitivity of the spin-mixing interferometry in a spinor BEC.

Curvature Energy and Their Spectrum in the Spinor-Twistor Framework: Torsion as Indicium of Gravitational Waves

The twistor kinematic-energy model of the space-time and the kinematic-energy tensor as the energy-matter tensor in relativity are considered to demonstrate the possible behavior of gravity as gravitational waves that derive of mass-energy source in the space-time and whose contorted image is the spectrum of the torsion field acting in the space-time. The energy of this field is the energy of their second curvature. Likewise, it is assumed that the curvature energy as spectral curvature in the twistor kinematic frame is the curvature in twistor-spinor framework, which is the mean result of this work. This demonstrates the lawfulness of the torsion as the indicium of the gravitational waves in the space-time. A censorship to detect gravitational waves in the space-time is designed using the curvature energy.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

与不同的一个改进非线性的 Schrödinger 方程平常在一个光格子的旋量鲍斯·爱因斯坦冷凝物(BEC ) 之一被小心地为旋转的概率振幅在运动的方程考虑一个非线性的术语获得。例如，模型的椭圆形的功能波浪答案在特定的边界状况下面被发现原子链的二结束被修理。在限制的情况中，椭圆形的函数波浪解决方案被简化为 spin-wave-like 或 solitons。

关于广义相对论的Brown-York与Quadratic Spinor作用量

广义相对论希尔伯特作用量在类空无穷远发散.如果要在类空无穷远得到收敛,则需要在希尔伯特作用量加上边界修正项.比较在类空无穷远收敛的Brown-York作用量,以及二次方旋量场(Quadratic Spinor)作用量.发现当狄拉克(Dirac)旋量场在边界超曲面上满足Witten方程时,二次方旋量场作用量在渐进类空无穷远等于Brown-York作用量.

Spinor Field Realizations of W2,6 String and W6 String

In this paper the spinor field BRST charges of the W2,6 string and W6 string are constructed, where the BRST charges are graded.

Quantum Correlation of Many Atoms in Spinor Bose-Einstein Condensates

在这个字母，我们在旋量 Bose 爱因斯坦冷凝物学习了 sub-Poissonian 分布和原子的量关联。在那里存在，这被发现为 spin-1 和旋转的 thesub-Poissonian 分布 --(-1) 部件分别地。可以在那里存在 Cauchy-Schwartz 不平等的违背。为一样的原子序数，，包括 Cauchy-Schwartz 不平等的违背的区域将为一样的 Rabi 频率与 Rabifrequency 的增长转移向右，这些区域将与原子序数的增长转移 leftwards。

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l + 1, l and l - 1,respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l+ 1, and l and l - 1. In this case the fluctuations are a constant,and the magnetic soliton appears.

Stochastic resonance of spinor condensates in optical cavity

Stochastic resonance is a phenomenon in which adding random noise to a system enhances the detection or transmission of a weak signal. It occurs when the noise interacts with the system's nonlinearity, thus improving signal-to-noise ratio and increasing sensitivity. Although parametric resonances in an atomic spinor Bose-Einstein condensate have been investigated, the question of whether one can observe stochastic resonance in such a system persists. In this study we propose a scheme for generating stochastic resonance in a cavity-spinor Bose-Einstein condensate coupling system. We demonstrate stochastic resonance through numerical calculations using the mean-field theory and truncated Wigner approximation methods. Furthermore, the characteristics of the system's response to noise and periodic signals are studied in detail. This study unravels a new scheme for observing stochastic resonance via linking atomic many-body physics with cavity quantum electrodynamics.

Bispinor Space

In this paper, we give identifications of bispinor space with Grassmann algebra, and with Clifford algebra. The multiplication in Clifford algebra provides an action on them. Lastly we have researched on the geometry of bispinor space, and define Dirac operators to get a Pythagoras equality.