The Branch Processes of Chern-Simons (CS) <Emphasis Type="Italic">p</Emphasis>-Branes

In this paper, by making use of Duan’s topological current theory, the branch process of Chern-Simons (CS) p-branes is discussed in detail. Chern-Simons (CS) p-branes are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points and higher degenerated points systematically of the vector order parameter field . Furthermore, it is also shown that CS p-branes are found splitting or merging at the degenerate point of field function but the total topological charges of the CS p-branes are still unchanged.     

Topological structure of Gauss-Bonnet-Chern theorem and -branes

By making use of the φ-mapping topological current theory, this paper shows that the Gauss-Bonnet-Chern density (the Euler-Poincaré characteristic χ(M) density) can be expressed in terms of a smooth vector field φ and take the form of δ(φ), which means that only the zeros of φ contribute to χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes.     

Vortex Lines and Monopoles in Electrically Conducting Plasmas

Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents, which can be derived from the same topological term n^→·（Эin^→×Эjn^→）, and both these topological structures axe characterized by the φ-mapping topological numbers-Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invaxiant is a proper topological invaxiant to describe the knotted solitons.     

A constraint on physical quantum states in cosmological space-times

The problem of constructing the Hilbert space of physical states for a free scalar quantum field propagating on a cosmological background is considered. The concept of energy-momentum for such a field is discussed and it is noted that, according to current renormalization theory, for a state ¦M to have finite energy density its associated anticommutator function must be of a particular form first discussed by Hadamard. This restriction is shown to lead to a constraint on the construction of the Hilbert space of physical states. This constraint is used to reject a recently proposed scheme for the construction of this space which was based on a principle of energy minimization.This essay received an honourable mention from the Gravity Research Foundation for the year 1984.-Ed.     

Topological Structure of Knotted Vortex Lines in Liquid Crystals

In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.     

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.     

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii-Moriya interaction.The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00 + sin θ |11 and cos |01 + sin |10 at zero temperature.The influences of Dzyaloshinskii-Moriya interaction D,anisotropic parameter and environment coupling strength γ on entanglement evolution are analysed in detail.It is found that the effect of noisy environment obviously suppresses the entanglement evolution,and the Dzyaloshinskii-Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos |01 + sin |10.Finally,a formula of steady state concurrence is obtained,and it is shown that the stable concurrence,which is independent of different initial states and Dzyaloshinskii-Moriya interaction D,depends on the anisotropic parameter and the environment coupling strength γ.     

Lattice systems with a continuous symmetry

We investigate a continuous Ising system on a lattice, equivalently an anharmonic crystal, with interactions: $$\sum\limits_{\left\langle {x,y} \right\rangle } {\left( {\phi _x - \phi _y } \right)} ^2 + \lambda \left( {\phi _x - \phi _y } \right)^4 , \phi _x \in \mathbb{R}, x \in \mathbb{Z}^d .$$ We prove that the perturbation expansion for the free energy and for the correlation functions is asymptotic about λ=0, despite the fact that the reference system (λ=0) does not cluster exponentially. The results can be extended to more general systems of this type, e.g. an even polynomial semibounded from below instead of a quartic interaction. By a suitable scaling, λ corresponds to the temperature.     

Nonlinear Schrödinger equations and sharp interpolation estimates

A sharp sufficient condition for global existence is obtained for the nonlinear Schrödinger equation $$\begin{array}{*{20}c} {(NLS)} & {2i\phi _t + \Delta \phi + \left| \phi \right|^{2\sigma } \phi = 0,} & {x \in \mathbb{R}^N } & {t \in \mathbb{R}^ + } \\ \end{array} $$ in the case σ=2/N. This condition is in terms of an exact stationary solution (nonlinear ground state) of (NLS). It is derived by solving a variational problem to obtain the “best constant” for classical interpolation estimates of Nirenberg and Gagliardo.     

KamLAND and solar antineutrino spectrum

We use the recent KamLAND observations to predict the solar antineutrino spectrum at some confidence limits. We find a scaling of the antineutrino probability with respect to the magnetic field profile—in the sense that the same probability function can be reproduced by any profile with a suitable peak field value—that can be utilized to obtain the general shape ofthe solar antineutrino spectrum. This scaling and the upper bound on the solar antineutrino event rate, which can be derived from the data, lead to: 1) an upper bound on the solar antineutrino flux and 2) the prediction of their energy spectrum. We get \(\phi _{\bar \nu } < 3.8 \times 10^{ - 3} \phi (^8 B)\) or \(\phi _{\bar \nu } < 5.5 \times 10^{ - 3} \phi (^8 B)\) at 95% C.L., assuming Gaussian or Poissonian statistics, respectively. For 90% C.L., these become \(\phi _{\bar \nu } < 3.4 \times 10^{ - 3} \phi (^8 B)\) and \(\phi _{\bar \nu } < 4.9 \times 10^{ - 3} \phi (^8 B)\). This provides an improvement by a factor of 3–5 with respect to the existing bounds. These limits are quite general and independent of the detailed structure of the magnetic field in the solar interior.     

Static finite energy solutions of a classical field theory with positive mass-square

Static finite energy solutions of the field theory described by are obtained. Some of the interesting features of this model are (1) the mass-square here is positive unlike in the λφ⁴ Higg's model, (2) the potential has three global minimas, (3) the spectrum is bounded from below unlike in the λφ⁴ theory with λ<0, (4) there are two kink and two antikink solutions, (5) unlike sine-Gordon and λφ⁴ models here there are two particles with masses m and 2m. Nontopological finite energy solutions have also been obtained for gφ ⁶ field theory with g < 3λ ² / 16m ².     

Structures of distorted phases and critical and noncritical atomic displacements of elpasolite Rb<Subscript>2</Subscript>KInF<Subscript>6</Subscript> during phase transitions

The structures of all three phases of the Rb₂KInF₆ crystal have been determined from the experimental X-ray diffraction data for the powder sample. The refinement of the profile and structural parameters has been carried out by the technique implemented in the DDM program, which minimizes the differences between the derivatives of the calculated and measured X-ray intensities over the entire profile of the X-ray diffraction pattern. The results obtained have been discussed using the group-theoretical analysis of the complete order-parameter condensate, which takes into account the critical and noncritical atomic displacements and permits the interpretation of the experimental data obtained previously. It has been reliably established that the sequence of changes in the symmetry during phase transitions in Rb₂KInF₆ can be represented as $ Fm\bar 3m\xrightarrow[{0,0,\phi }]{{11 - 9\left( {\Gamma _4^ + } \right)}}{{I114} \mathord{\left/ {\vphantom {{I114} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}}} \right. \kern-\nulldelimiterspace} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}} $ Fm\bar 3m\xrightarrow[{0,0,\phi }]{{11 - 9\left( {\Gamma _4^ + } \right)}}{{I114} \mathord{\left/ {\vphantom {{I114} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}}} \right. \kern-\nulldelimiterspace} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}} .     

Lattice systems with a continuous symmetry

We consider perturbations of a massless Gaussian lattice field on ? ^d ,d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., $$ - H = \sum\limits_{< x,y > } {(\phi _x - \phi _y )^2 + T(\phi _x - \phi _y )^4 ,\phi _x \in \mathbb{R}.} $$ It is known that for allT>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities.     

Search for rare radiative decays ofΦ-meson at VEPP-2M

Results of the search for rare radiative decay modes of the ?-meson performed with the Neutral Detector at the VEPP-2M collider are presented. For the first time upper limits for the branching ratios of the following decay modes have been placed at 90% confidence level: $$\begin{gathered} B(\phi \to \eta '\gamma )< 4 \cdot 10^{ - 4} , \hfill \\ B(\phi \to \pi ^0 \pi ^0 \gamma )< 10^{ - 3} , \hfill \\ B(\phi \to f_0 (975)\gamma )< 2 \cdot 10^{ - 3} , \hfill \\ B(\phi \to H\gamma )< 3 \cdot 10^{ - 4} , \hfill \\ \end{gathered} $$ whereH is a scalar (Higgs) boson with a mass 600 MeV<m _H <1000 MeV, the real measurement isB(φ→H γ)·B(H→2π⁰)<0.8·10^-4, the quoted result is model dependent, as explained in the text, $$\begin{gathered} B(\phi \to a\gamma ) \cdot B(a \to e^ + e^ - )< 5 \cdot 10^{ - 5} , \hfill \\ B(\phi \to a\gamma ) \cdot B(a \to \gamma \gamma )< 2 \cdot 10^{ - 3} , \hfill \\ \end{gathered} $$ wherea is a particle with a low mass and a short lifetime, $$B(\phi \to a\gamma )< 0.7 \cdot 10^{ - 5} ,$$ wherea is a particle with a low mass not observed in the detector.     

The topological structure of the integral quantum Hall effect in magnetic semiconductor-superconductor hybrids

An unconventional integer quantum Hall regime was found in magnetic semiconductor-superconductor hybrids. By making use of the decomposition of the gauge potential on a U(1) principal fibre bundle over k-space, we study the topological structure of the integral Hall conductance. It is labeled by the Hopf index β and the Brouwer degree η. The Hall conductance topological current and its evolution is discussed.     

Reconstructing dark energy potentials from parameterized deceleration parameters

In this paper, the properties of dark energy are investigated according to the parameterized deceleration parameter q(z), which is used to describe the extent of the accelerating expansion of the universe. The potential of dark energy V(φ) and the cosmological parameters, such as the dimensionless energy density \varOmega_φ, \varOmega_m, and the state parameter w_φ, are connected to it. Concretely, by giving two kinds of parameterized deceleration parameters q(z)=a+bz/(1+z) and q(z)=1/2+(az+b)/(1+z)^2, the evolution of these parameters and the reconstructed potentials V(φ) are plotted and analysed. It is found that the potentials run away with the evolution of universe.     

The Lipatov argument

Lipatov's argument gives a formula for evaluating asymptotically the large order perturbation coefficients for the anharmonic oscillator or (φ⁴) quantum field models. We give a partial justification of the argument which enables us to prove that the radius of convergence of the Borel transform of the pressure for lattice φ⁴ models given by $$\exp \left[ {\mathop {\inf }\limits_\phi \left\{ {\tfrac{1}{2}\sum\limits_j {\left[ {(\nabla \phi )^2 (j) + \phi (j)^2 } \right] - \log } \sum {\phi (j)^4 } } \right\} - 2} \right].$$      

High energy electron radiation effect on Ni and Ti/4H-SiCSchottky barrier diode at room temperature

This paper reports that Ni and Ti/4H-SiC Schottky barrier diodes (SBDs) were fabricated and irradiated with 1~MeV electrons up to a dose of 3.43×10¹⁴~e/cm². After radiation, the Schottky barrier height φ _B of the Ni/4H-SiC SBD increased from 1.20~eV to 1.21~eV, but decreased from 0.95~eV to 0.94~eV for the Ti/4H-SiC SBD. The degradation of φ _B could be explained by interface states of changed Schottky contacts. The on-state resistance R_S of both diodes increased with the dose, which can be ascribed to the radiation defects. The reverse current of the Ni/4H-SiC SBD slightly increased, but for the Ti/4H-SiC SBD it basically remained the same. At room temperature, φ _B of the diodes recovered completely after one week, and the R_S partly recovered.     

Transmission of electron through an Aharonov－Bohm interferometer with a quantum dot in Coulomb blockade regime

We calculate conductance of an Aharonov－Bohm (AB) interferometer for which a single-level quantum dot in the Coulomb blockade regime is embedded in one of its arms. Using the Schr?dinger equations and taking into account the Coulomb interaction on the dot, we calculate conductance G as a function of flux φ threaded through the ring and as a function of gate voltage V applied to the dot. It is found that the AB oscillations of G(φ) depend on the particle occupation on the dot, controlled by V. If the system is closed, there is no loss of particles, G(φ) is periodic and G(φ)=G(-φ), satisfying the Onsager relation. In this case G(φ) can reach its maximum value, 2e^2/h, at the resonance. When the system is open, one has G(φ)≠G(-φ), G(φ) yields a phase shift which depends on the loss rate of electrons in this open system.     

Spherically Symmetric Solutions of Light Galileon

We have been studied the model of light Galileon with translational shift symmetry ? → ? + c. The matter Lagrangian is presented in the form \(\mathcal {L}_{\phi }= -\eta (\partial \phi )^{2}+\beta G^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi \). We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of \(f(R,R^{\mu \nu }T_{\mu \nu }^{m})\). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon’s field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ? = t, which it is remembered by us dilaton field.