Fabrication of Two-Dimensional Photonic Crystals with Triangular Rods by Single-Exposure Holographic Lithography

We demonstrate a single-exposure holographic fabrication of two-dimensional photonic crystal with round- cornered triangular ＇atoms＇ arranged in a triangular lattice. Simulation results show that double absolute photonic band gaps exist in this structure. Our experimental results show that holographic lithography can be used to fabricate photonic crystals not only with various lattice structures but also with various kinds of structures of the atoms, to obtain absolute band gaps or a particular band gap structure. Furthermore, the single-exposure holographic method not only makes the fabrication process simple and convenient but also makes the structures of the atoms more perfect.     

Improved Microfluidic Coupled-Cavity Waveguides for Slow Light Transmission

We present a method based on the selective liquid infiltration in air holes to produce slow light in a coupled-cavity waveguide structured by two-dimensional photonic crystal and analyze the slow light propagation in the coupled-cavity waveguide with triangular lattice. The group velocity profile of different coupled-cavity waveguides, obtained by the selective liquid infiltration in the holes between the cavities in waveguide and the increased radius of the first row of holes adjacent to the waveguide, is evaluated by using both the plane-wave expansion method and a tight binding model. We determine the optimal parameters to reduce the group velocity. Using a simpler coupled-cavity waveguide structure we obtain smaller group velocity compared to most investigations.     

Diverse solid and supersolid phases of bosons in a triangular lattice

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.     

Ashkin-Teller Formalism for Elastic Response of DNA Molecule to External Force and Torque

We propose an Ashkin-Teller-like model for elastic response of DNA molecule to external force and torque. The base-stacking interaction is described in a simple and uniform way. We obtain the phase diagram of dsDNA, and in particular, the transition from 13 form to the S state induced by stretching and twisting. The elastic response of the ssDNA is presented also in a unified formalism. The close relation of dsDNA molecule structure with elastic response is shown clearly. The calculated folding angle of the dsDNA molecule is 59.2°.     

Eigenvalue Problems of non-Hermitian Systems via Improved Asymptotic Iteration Method

We simply use the relation between the asymptotic iteration method and the Nikiforov-Uvarov method for the analytical solution of the second order linear ordinary differential equations. We apply this relation to study the Schroedinger equation with potentials admitting quasinormal modes. Non-Hermitian PT symmetric potentials have also been studied. Energy eigenvalues in all the cases by the relation are found to be consistent with exact results.     

Tow—Dimensional Micro—grating Formed by Polystyrene Spheres

We report a simple method to make two-dimensional plane gratings that can be used as splitters. In the self-assembly process, the colloidal spheres can form single layer square or triangular lattice on a fiat surface and in our experiments the triangular lattice is a more common structure. As an incident beam passes through the triangular lattice, it can be split into seven sub-beams, among which six beams have the same density and scattering angle. This grating is not sensitive to the polarization direction of the incident light.     

The symmetry group of Feynman diagrams and consistency of the BPHZ renormalization scheme

We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams.We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the interaction Hamiltonian in all cases,including that of Feynman diagrams with symmetry factors.     

The angular momentum and parity projected multidimensionally constrained relativistic Hartree–Bogoliubov model

Nuclear deformations are fundamentally important in nuclear physics.We recently developed a multidimensionally constrained relativistic Hartree-Bogoliubov(MDCRHB)model,in which all multipole deformations respecting the V₄ symmetry can be considered self-consistently.In this work we extend this model by incorporating the angular momentum projection and parity projection to restore the rotational and parity symmetries broken in the mean-field level.This projected MDCRHB(p-MDCRHB)model enables us to connect certain nuclear spectra to exotic intrinsic shapes such as triangles or tetrahedrons.We present the details of the method and an exemplary calculation for ¹²C.We develop a triangular moment constraint to generate the triangular configurations consisting of three α clusters arranged as an equilateral triangle.The resulting ¹²C spectra are consistent with that from a triangular rigid rotor for large separations between the α clusters.We also calculate the B(E2)and B(E3)values for low-lying states and find good agreement with the experiments.     

Electron Backscattered Diffraction of Transgranular Crack Propagation in Soft Steel

We consider the crack propagation in a soft steel sheet during the formation. The drawability is considered in relation with the structural anisotropy, the mechanical behaviour is related to both the grain morphology and the texture. The structure heterogeneity could lead to the apparition of micro-cracks. The results show the texture effect on the crack propagation and on the crack arrest in soft steel during the formation. The EBSD technique allows to show that the adjustment of the grain orientation from the initial main component {111}（112） towards the deformation orientation {111}（110） incites a trans-granular crack through a grain with initial {111}（112） orientation in a globally ductile material. It is the presence of grains with {111}（110） orientation which permits the closing of micro-cracks.     

Magnetic Field Structure and Induced Electric Current Distribution on a Cylindrical Model： Application to Magnetic Nerve Stimulation

We study the relation between the magnetic field structure and the induced electric-current distribution based on a cylindrical model composed of a uniform electrically conductive medium. When the time-varying magnetic fields are axisymmetrically applied in the axial direction of the model, the electric fields are induced around the central axis in accordance with Faradays law. We examine the eddy-current distributions generated by loop-coils with various geometries carrying an alternating electric current. It is shown that the radial structure of the induced fields can significantly be controlled by the loop coil geometry, which will be suitable for practical use especially in magnetic nerve stimulation on bioelectromagneties, if we appropriately p/ace the exciting coil with optimum geometry.     

Large Seebeck coefficient resulting from chiral interactions in triangular triple quantum dots

We theoretically study thermoelectric transport properties through a triangular triple-quantum-dot (TTQD) structure in the linear response regime using the hierarchical equations of motion approach. It is demonstrated that large Seebeck coefficient can be obtained when properly matching the interdot tunneling strength and magnetic flux at the electron-hole symmetry point, as a result of spin chiral interactions in the TTQD system. We present a systematic investigation of the thermopower (the Seebeck coefficient) dependence on the tunneling strength, magnetic flux, and on-site energy. The Seebeck coefficient shows a clear breakdown of electron-hole symmetry in the vicinity of the Kondo regime, accompanied by the deviation from the semiclassical Mott relation in the Kondo and mixed-valence regimes, which result from the many-body effects of the Kondo correlated induced resonance together with spin chiral interactions.     

Symmetry of Lyapunov spectrum

The symmetry of the spectrum of Lyapunov exponents provides a useful quantitative connection between properties of dynamical systems consisting ofN interacting particles coupled to a thermostat, and nonequilibrium statistical mechanics. We obtain here sufficient conditions for this symmetry and analyze the structure of 1/N corrections ignored in previous studies. The relation of the Lyapunov spectrum symmetry with some other symmetries of dynamical systems is discussed.     

Observation of shear-wave Mach cones in a 2D dusty-plasma crystal

Mach cones composed of shear waves were observed experimentally in a two-dimensional screened-Coulomb crystal. Highly charged microspheres suspended in a plasma and interacting with a repulsive Yukawa potential arranged themselves in a triangular lattice with hexagonal symmetry. Mach cones were excited by applying a force from the radiation pressure of a moving laser beam. They had a single-cone structure, which is explained by the almost dispersionless character of shear waves. The cone's opening angle obeyed the Mach-cone-angle relation. Results are compared to a molecular-dynamics simulation.     

圆环结构磁光光子晶体中的拓扑相变

二维圆环结构的三角晶格磁光光子晶体中可以呈现多重拓扑相.在不同的几何参数和磁场下,这些拓扑相包括正常光子带隙相、量子自旋霍尔相和反常量子霍尔相.与文献[1]类似,该结果展现了二维光子晶体丰富的拓扑相变现象.     

Check of AGT relation for conformal blocks on sphere

The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves propagators and vertices. We evaluated vertices with two Virasoro algebra descendants and explicitly checked the AGT relation up to the third order of the expansion for the 5-point and 6-point conformal blocks on sphere confirming all the predictions of arXiv:0906.3219 relevant in this situation. We propose that U(1)$U(1)$-factor can be extracted from the matrix elements of the free field vertex operators. We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.     

Direct transition from a disordered to a multiferroic phase on a triangular lattice

We report the first direct transition from a paramagnetic and paraelectric phase to an incommensurate multiferroic in the triangular lattice antiferromagnet RbFe(MoO4)(2). Ferroelectricity is observed only when the magnetic structure has chirality and breaks inversion symmetry. A Landau expansion of symmetry-allowed terms in the free energy demonstrates that chiral magnetic order can give rise to a pseudoelectric field, whose temperature dependence agrees with experiment.     

Hecke Symmetries and Characteristic Relations on Reflection Equation Algebras

We analyze the relation between the properties of Hecke symmetry (i.e., Hecke type R-matrix) and the algebraic structure of the corresponding reflection equation (RE) algebra. Analogues of the Newton relations and Cayley–Hamilton theorem for the matrix of generators of the RE algebra associated with a finite rank even Hecke symmetry are derived.