On strong convergence to 3-D axisymmetric vortex sheets

We consider the 3-D axisymmetric incompressible Euler equations without swirls with vortex-sheets initial data. It is proved that the approximate solutions, generated by smoothing the initial data, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This implies that if there would appear singularity or energy lost in the process of limit for the approximate solutions, it then must happen in the region away from the symmetry axis. There is no restriction on the signs of initial vorticity here. In order to exclude the possible concentrations on the symmetry axis, we use the special structure of the equations for axisymmetric flows and careful choice of test functions.     

Local Unitary Invariants for Multipartite States

We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full rank mixed states with non-degenerate eigenvalues, this set of invariants is also the set of the necessary and sufficient conditions for the local unitary equivalence of such two states.     

A Note on Resistance of NPT to Mixture of Separable States

We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number n (n>1) which is NPT, we show that this state is still NPT when it is mixed with no more than $\frac {n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case.     

Dynamics of Quantum Correlations for Atoms in Independent Single-Mode Cavity

We investigate the dynamics of two identical atoms resonantly coupled to independent single-mode cavity in zero detuning without rotating wave approximation (RWA). It is shown that for two atoms initially in the ground state, the entanglement (concurrence) and the normalized geometric measure of quantum discord (NGMQD) display similar behavior. There is no sudden death and sudden birth. And the entanglement is always larger than NGMQD in this case. For two atoms initially in excited state, one can see the novel entanglement sudden death (ESD) and sudden birth (ESB) phenomena. The entanglement is not always greater than the NGMQD in this case. Consequently, there is no simple dominance relation between the entanglement and the NGMQD.     

普通物理综合设计实验课教学方法改革初探

开设普通物理综合设计实验课程目的在于培养学生动手能力、分析问题解决问题能力和创新能力。本文以首都师范大学物理系开设的普通物理综合设计实验为例讨论了具体的教学方法和过程,首先通过设计大量的预习思考题提高学生预习的针对性和预习效果,通过分组讨论来理解实验原理,并给出设计思路,最后通过实际实验锻炼学生的动手能力。该方法取得了良好的教学效果。     

Quantum phases,supersolids and quantum phase transitions of interacting bosons in frustrated lattices

By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from 1/3 (2/3) filling on frustrated lattices such as triangular and Kagome lattice. In a triangular lattice at 1/3, we find a X-CDW, a stripe CDW phase which was found previously by a density operator formalism (DOF). Most importantly, we also find a new CDW-VB phase which has both local CDW and local VB orders, in sharp contrast to a bubble CDW phase found previously by the DOF. In the Kagome lattice at 1/3, we find a VBS phase and a 6-fold CDW phase. Most importantly, we also identify a CDW-VB phase which has both local CDW and local VB orders which was found in previous QMC simulations. We also study several other phases which are not found by the DVM. By analyzing carefully the saddle point structures of the dual gauge fields in the translational symmetry breaking sides and pushing the effective actions slightly away from the commensurate filling f=1/3$f=1/3$(2/3)$(2/3)$, we classified all the possible types of supersolids and analyze their stability conditions. In a triangular lattice, there are X-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. In a Kagome lattice, there are 6-fold CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. We show that independent of the types of the SS, the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents z=2$z=2$, ν=1/2$\nu =1/2$, η=0$\eta =0$ (with logarithmic corrections). Excitation spectra of all these insulating phases and supersolid phases are also studied. Implications on QMC simulations with both nearest neighbor and next nearest neighbor interactions in both lattices are given. Some possible intrinsic problems of the DOF in identifying the insulating phases are also pointed out.     

Fundamental groups of positively curved manifolds with symmetry

We obtain a classification for the fundamental groups of closed $n$ -manifolds of positive sectional curvature which admit an isometric $T^k$ -action with $k \ge \frac{n}{6}+1 (n \ne 11, 15)$ .     

Higher algebraic K-groups and {\mathcal D}-split sequences

In this paper, we use ${\mathcal D}$ -split sequences and derived equivalences to provide formulas for calculation of higher algebraic K-groups (or mod-p K-groups) of certain matrix subrings which occur both in commutative algebra as the endomorphism rings of direct sums of Prüfer modules or of chains of Glaz–Vasconcelos ideals and in noncommutative geometry as an essential ingredient of the study of singularities of orders over surfaces. In our results, we do not assume any homological requirements on rings and ideals under investigation, and therefore extend sharply many existing results of this type in the algebraic K-theory literature to a more general context.     

A class of antimagic join graphs

A labeling f of a graph G is a bijection from its edge set E(G) to the set {1, 2, . . . , |E(G)|}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K 2 is antimagic. In this paper, we show that if G 1 is an n-vertex graph with minimum degree at least r, and G 2 is an m-vertex graph with maximum degree at most 2r-1 (m ≥ n), then G1 ∨ G2 is antimagic.     

On a supersymmetric nonlinear integrable equation in (2+1) dimensions

A supersymmetric integrable equation in (2+1) dimensions is constructed by means of the approach of the homogenous space of the super Lie algebra, where the super Lie algebra osp(3/2) is considered. For this (2+1) dimensional integrable equation, we also derive its Bäcklund transformation.