Topology of Knotted Optical Vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the Duan＇s topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.     

Ferromagnetic-insulators-modulated transport properties on the surface of a topological insulator

Transport properties on the surface of a topological insulator （TI） under the modulation of a two-dimensional （2D） ferromagnet/ferromagnet junction are investigated by the method of wave function matching. The single ferromagnetic barrier modulated transmission probability is expected to be a periodic function of the polarization angle and the planar rotation angle, that decreases with the strength of the magnetic proximity exchange increasing. However, the transmission probability for the double ferromagnetic insulators modulated n-n junction and n-p junction is not a periodic function of polarization angle nor planar rotation angle, owing to the combined effects of the double ferromagnetic insulators and the barrier potential. Since the energy gap between the conduction band and the valence band is narrowed and widened respectively in ranges of 0 ≤ 0 〈π/2 and r/2 〈 0 ≤ π, the transmission probability of the n-n junction first increases rapidly and then decreases slowly with the increase of the magnetic proximity exchange strength. While the transmission probability for the n-p junction demonstrates an opposite trend on the strength of the magnetic proximity exchange because the band gaps contrarily vary. The obtained results may lead to the possible realization of a magnetic/electric switch based on TIs and be useful in further understanding the surface states of TIs.     

Topological structure of the solitons solution in SU（3） Dunne-Jackiw-Pi-Trugenberger model

By using C-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU（N） Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU（3） case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of C-mapping. In our solution, the flux of this soliton is naturally quantized.     

Knotted Topological Phase Singularities of Electromagnetic Field

In this paper, knotted objects （RS vortices） in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the Duan＇s topological current theory, we rewrite the topological current form of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum of the linking and self-linking numbers of the knotted RS vortices. Furthermore, the conservation of the Hopf invariant in the splitting, the mergence and the intersection processes of knotted RS vortices is also discussed.     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

Knotted Solitons in an Interacting Mixture of a Charged and a Neutral Superfluid for Neutron Stars

By making use of the decomposition of U（1） gauge potential theory and the C-mapping method we discuss a mixture of interacting neutral and charged Bose condensates, which is supposed being realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We propose that this system possesses vortex lines and two classes of knotted solitons. The topological charge of the vortex lines are characterized by the Hopf indices and the Brower degrees of φ-mapping, and the knotted solitons are described by nontrivial Hopf invariant and the BF action respectively.     

Ferromagnetic barrier-induced negative differential conductance on the surface of a topological insulator

The effect of the negative differential conductance of a ferromagnetic barrier on the surface of a topological insulat（ is theoretically investigated. Due to the changes of the shape and position of the Fermi surfaces in the ferromagnetic barrie the transport processes can be divided into three kinds： the total, partial, and blockade transmission mechanisms. The bias voltage can give rise to the transition of the transport processes from partial to blockade transmission mechanisms, which results in a considerable effect of negative differential conductance. With appropriate structural parameters, the currenl voltage characteristics show that the minimum value of the current can reach to zero in a wide range of the bias voltag and then a large peak-to-valley current ratio can be obtained.     

Electron states scattering off line edges on the surface of topological insulator

We study the local density of states （LDOS） for electrons scattering off the line edge of an atomic step defect on the surface of a three-dimensional （3D） topological insulator （TI） and the line edge of a finite 3D TI, where the front surface and side surface meet with different Fermi velocities, respectively. By using a S-function potential to model the edges, we find that the bound states existed along the step line edge significantly contribute to the LDOS near the edge, but do not modify the exponential behavior away from it. In addition, the power-law decaying behavior for LDOS oscillation away from the step is understood from the spin rotation for surface states scattering off the step defect with magnitude depending on the strength of the potential. Furthermore, the electron refraction and total reflection analogous to optics occurred at the line edge where two surfaces meet with different Fermi velocities, which leads to the LDOS decaying behavior in the greater Fermi velocity side similar to that for a step line edge. However, in the smaller velocity side the LDOS shows a different decaying behavior as x-1/2, and the wavevector of LDOS oscillation is no longer equal to the diameter of the constant energy contour of surface band, but is sensitively dependent on the ratio of the two Fermi velocities. These effects may be verified by STM measurement with high precision.     

A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings

In this note we make a test of the open topological string version of the OSV conjecture in the toric Calabi-Yau manifold X = O（-3） → P^2 with background D4-branes wrapped on Lagrangian submanifolds. The Dbrahe partition function reduces to an expectation value of some inserted operators of a q-deformed Yang Mills theory living on a chain of P^1 ＇s in the base p2 of X. At large N this partition function can be written as a sum over squares of chiral blocks, which are related to the open topological string amplitudes in the local p2 geometry with branes at both the outer and inner edges of the toric diagram. This is in agreement with the conjecture.     

Ferromagnetism on a paramagnetic host background in cobalt-doped Bi_2Se_3 topological insulator

Cobalt-doped Bi2Se3topological insulators have been grown though melt-grown reaction. The Bi2Se3matrix is diamagnetic and doped sample is a superposition of ferromagnetism(FM) and paramagnetism(PM) behavior at low temperature. The values of MSmol, Hc, and Mr increase as the Co concentration increases. Two possible explanations have been proposed for the origin of ferromagnetism in Co-doped Bi2Se3. One is the magnetic ordering from nanoclusters of Co–Se compound in the crystals, and the other is Ruderman–Kittel–Kasuya–Yosida(RKKY) interaction between magnetic impurities.     

Collective behaviors of suprachiasm nucleus neurons under different light–dark cycles

The principal circadian clock in the suprachiasm nucleus(SCN) regulates the circadian rhythm of physiological and behavioral activities of mammals. Except for the normal function of the circadian rhythm, the ensemble of SCN neurons may show two collective behaviors, i.e., a free running period in the absence of a light–dark cycle and an entrainment ability to an external T cycle. Experiments show that both the free running periods and the entrainment ranges may vary from one species to another and can be seriously influenced by the coupling among the SCN neurons. We here review the recent progress on how the heterogeneous couplings influence these two collective behaviors. We will show that in the case of homogeneous coupling, the free running period increases monotonically while the entrainment range decreases monotonically with the increase of the coupling strength. While in the case of heterogenous coupling, the dispersion of the coupling strength plays a crucial role. It has been found that the free running period decreases with the increase of the dispersion while the entrainment ability is enhanced by the dispersion. These findings provide new insights into the mechanism of the circadian clock in the SCN.     

Physical design of a wavelength tunable fully coherent VUV source using a self-seeding free electron laser

In order to meet the requirements of the synchrotron radiation users, a fully coherent VUV free electron laser （FEL） has been preliminarily designed. One important goal of this design is that the radiation wavelength can be easily tuned in a broad range （70 170 nm）. In the light of the users＇ demand and our actual conditions, the self-seeding scheme is adopted for this proposal. Firstly, we attempted to fix the electron energy and only changed the undulator gap to vary the radiation wavelength; however, our analysis implies that this is difficult because of the great difference of the power gain length and FEL efficiency at different wavelengths. Therefore, we have considered dividing the wavelength range into three subareas. In each subarea, a constant electron energy is used and the wavelength tuning is realized only by adjusting the undulator gap. The simulation results show that this scheme has an acceptable performance.     

Hadro- and photo-production of η′ in quasi-free proton and neutron processes

The η′ photoproduction process on quasi-free proton and neutron and the reaction NN→ η′NN are investigated within a relativistic effective Lagrangian approach to hadronic interactions. Resonances with spins 1/2 and 3/2 are considered together with the nucleonic and t-channel meson-exchange current contributions. In photoproduction processes, the S11 resonance is found to be responsible for the sharp rise of the cross sections near threshold. In pp → η′pp, it is found that the S11 resonance dominates the total cross section over the entire energy region considered. The spin observables, in particular the beam and target asymmetries, are shown to be very sensitive to the reaction mechanism and will help impose more stringent constraints on the model parameters.     

Single Production of Top Quark via e-γ Collision in Left-Right Twin Higgs Model

In the context of the left-right twin Higgs （LRTH） model, we fist study single production of the standard model （SM） top quark via e-γ collisions. We find that the corrections of the LRTH model to the cross section of the process e-γ→vebt might be observed only for f ≤750 GeV and the heavy top quark mass scale M ≥500 GeV in future high energy linear e^＋e^- collider （LC） experiment with the center-of-mass （CM） energy √s = 500 GeV and a yearly integrated luminosity of ￡ = 100 fb^-1. We also consider single production of the heavy top quark T via e-γ collisions. Our numerical results show that the possible signals of the heavy top quark T might be observed via the decay channel T →Ф^＋b→tbb in future LC experiment with √s = 3 TeV and ￡ = 500 fb^-1.     

An analysis of undulator optimization in self-seeding free electron lasers

A simple analysis is given for the optimum length of undulator in a self-seeding free electron laser （FEL）. The obtained relations show the correlation between the undulator length and the system parameters. The power required for the seeding in the second part of the undulator and the overall efficiency of monochromatizating the seeding determine the length of the first part of the undulator; the magnitude of seeding power dominates the length of the second part of the undulator; the whole length of the undulator in a self-seeding FEL is determined by the overall efficiency for getting coherent seed, and is about half as long again as that of SASE, not including the dispersion section. The requirement of the dispersion section strength is also analyzed.     

Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates

The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.     

De Haas-van Alphen Effect of Free Electron Gas Revisited

The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.     

拓扑荷在圆盘状向列相液晶薄膜中的尺寸效应

拓扑现象对于病毒颗粒的空间分布、高分子聚合物纳米囊泡的成型以及玻色-爱因斯坦凝聚物等方面都发挥着重要作用.本文利用Landau-de Gennes理论,构建模型来模拟液晶中拓扑荷分布及其他现象.通过对数值模型序参量场的演化,以及模拟液晶薄膜中所生成的拓扑荷之间的相互作用来分析液晶(Lqc)薄膜的尺寸对拓扑荷的影响.研究结果表明,随着液晶盘半径增大,拓扑荷间最优距离与半径之比渐增并趋于稳定.此研究结论对利用拓扑荷凝聚颗粒物效应设计分离容器有指导意义,有助于进一步理解拓扑胶体和液晶以及液晶共聚物等软物质中的拓扑现象.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.     

Remarks on interpretations of the Eotvos experiment and misinterpretation of E=mc^2

The Eotvos experiment on the verification of equivalence between inertial mass and gravitational mass of a body is famous for its accuracy. A question is, however, can these experimental results be applied to the case of a physical space in general relativity, where the space coordinates could be arbitrary？ It is pointed out that it can be validly applied because it has been proven that Einstein＇s equivalence principle for a physical space must have a frame of reference with the Euclidean-like structure. Will claimed further that such an overall accuracy can be translated into an accuracy of the equivalence between inertial mass and each type of energy. It is shown that, according to general relativity, such a claim is incorrect. The root of this problem is due to an inadequate understanding of special relativity that produced the famous equation E=mc^2, which must be understood in terms of energy conservation. Concurrently, it is pointed out that this error is a problem in Will＇s book, ‘Theory and Experiment in Gravitational Physics＇.