Topological aspect of Chern--Simons p-branes

By generalizing the topological current of Abelian Chern--Simons (CS) vortices, we present a topological tensor current of CS p-branes based on the \phi -mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field \phi(x), and the topological structure of CS p-branes is characterized by the winding number of the \phi-mappings. Furthermore, the Nambu--Goto action and the equation of motion for multi CS p-branes are obtained.     

Efficient and stable wireless power transfer based on the non-Hermitian physics

As one of the most attractive non-radiative power transfer mechanisms without cables,efficient magnetic resonance wireless power transfer(WPT)in the near field has been extensively developed in recent years,and promoted a variety of practical applications,such as mobile phones,medical implant devices and electric vehicles.However,the physical mechanism behind some key limitations of the resonance WPT,such as frequency splitting and size-dependent efficiency,is not very clear under the widely used circuit model.Here,we review the recently developed efficient and stable resonance WPT based on non-Hermitian physics,which starts from a completely different avenue(utilizing loss and gain)to introduce novel functionalities to the resonance WPT.From the perspective of non-Hermitian photonics,the coherent and incoherent effects compete and coexist in the WPT system,and the weak stable of energy transfer mainly comes from the broken phase associated with the phase transition of parity-time symmetry.Based on this basic physical framework,some optimization schemes are proposed,including using nonlinear effect,using bound states in the continuum,or resorting to the system with high-order parity-time symmetry.Moreover,the combination of non-Hermitian physics and topological photonics in multi-coil system also provides a versatile platform for long-range robust WPT with topological protection.Therefore,the non-Hermitian physics can not only exactly predict the main results of current WPT systems,but also provide new ways to solve the difficulties of previous designs.     

Metastable state and macroscopic quantum tunneling of binary mixtures

We provide a mixing model to explore the metastable state and the macroscopic quantum tunneling (MQT) of binary mixtures. For , we first observe the two condensates form the symmetry-breaking state (SBS) and then suddenly transfer to the symmetry-preserving state (SPS) through the MQT. The SBS is shown to be the metastable state in our system. We find the MQT does not spontaneously arise. The inducement mechanism is the damping but not the excitations. The damping mechanism can also control the lifetime and the tunneling decay rate of the SBS. Finally, we further present the origin of these phenomena by examining the energy of the system.     

HNO二聚体蓝移氢键的理论研究

利用分子轨道从头算理论和密度泛函理论结合不同理论基组对于N-H…O蓝移氢键进行了详细的研究.利用标准方法和均衡校正方法对二聚体进行了几何优化,振动频率和相互作用能的计算.拓扑学和自然键轨道理论对于蓝移氢键的本质进行分析.自然键轨道(NBO)分析表明,σ*(N-H)轨道上电子密度降低是电子密度重排效应的结果.分子内电子重排、轨道再杂化和电子受体内部结构重组共同作用结果导致了N-H的振动频率大幅蓝移现象的出现.     

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional mean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezzè et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.     

Composite optical vortices in noncollinear Laguerre--Gaussian beams and their propagation in free space

Taking two Laguerre-Gaussian beams with topological charge 1 = ±1 as an example, this paper studies the composite optical vortices formed by two noncollinear Laguerre-Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio ξ, or off-axis distance ratio μ. The net topological charge lnet is not always equal to the sum lsum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane.     

Coherence properties of a Bose-Einstein condensate in an optical superlattice

We study the effect of a one dimensional optical superlattice on the superfluid properties (superfluid fraction, number squeezing, dynamic structure factor) and the quasi-momentum distribution of the Mott-insulator. We show that due to the secondary lattice, there is a decrease in the superfluid fraction and the number fluctuation. The dynamic structure factor which can be measured by Bragg spectroscopy is also suppressed due to the addition of the secondary lattice. The visibility of the interference pattern (the quasi-momentum distribution) of the Mott-insulator is found to decrease due to the presence of the secondary lattice. Our results have important implications in atom interferometry and quantum computation in optical lattices.     

Loop Groups and Twin Buildings

In these notes we describe some buildings related to complex Kac–Moody groups. First we describe the spherical building of SL_n() (i.e. the projective geometry PG(ⁿ)) and its Veronese representation. Next we recall the construction of the affine building associated to a discrete valuation on the rational function field (z). Then we describe the same building in terms of complex Laurent polynomials, and introduce the Veronese representation, which is an equivariant embedding of the building into an affine Kac–Moody algebra. Next, we introduce topological twin buildings. These buildings can be used for a proof which is a variant of the proof by Quillen and Mitchell, of Bott periodicity which uses only topological geometry. At the end we indicate very briefly that the whole process works also for affine real almost split Kac–Moody groups.Supported by a Heisenberg fellowship by the Deutsche Forschungsgemeinschaft.