Evidence of spin liquid with hard-core bosons in a square lattice

We show that laser assisted hopping of hard core bosons in a square optical lattice can be described by an antiferromagnetic $J_{1}$-$J_{2}$ XY model with tunable ratio of $J_{2}/J_{1}$. We numerically investigate the phase diagram of the $J_{1}$-$J_{2}$ XY model using both the tensor network algorithm for infinite systems and the exact diagonalization for small clusters and find strong evidence that in the intermediate region around $$, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Neel state on the $J_{2}\ll J_{1}$ side and the stripe antiferromagnetic phase on the $$ side. This finding opens up the possibility of studying the exotic spin liquid phase in a realistic experimental system using ultracold atoms in an optical lattice.Comment: 5 pages, 5 figure

Supersolid and charge density-wave states from anisotropic interaction in an optical lattice

We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well controlled numerical method based on the tensor network algorithm, we calculate phase diagram of the resultant effective Hamiltonian in a two-dimensional square lattice - an anisotropic Hubbard model of hard-core bosons with attractive interaction in one direction and repulsive interaction in the other direction. Besides the conventional superfluid and the Mott insulator states, we find the striped and the checkerboard charge density wave states and the supersolid phase that interconnect the superfluid and the striped solid states. The transition to the supersolid phase has a mechanism different from the case of the soft-core Bose Hubbard model.Comment: 5 pages, 5 figures

Topology of Knotted Optical Vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the $\phi$-mapping 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.Comment: 11 pages, no figures, accepted by Commun. Theor. Phys. (Beijing, P. R. China

Evolution of the Chern-Simons Vortices

Based on the gauge potential decomposition theory and the $\phi$-mapping theory, the topological inner structure of the Chern-Simons-Higgs vortex has been showed in detail. The evolution of CSH vortices is studied from the topological properties of the Higgs scalar field. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the scalar field $\phi .$Comment: 10 pages, 10 figure

Disclination in Lorentz Space-Time

The disclination in Lorentz space-time is studied in detail by means of topological properties of $\phi$-mapping. It is found the space-time disclination can be described in term of a Dirac spinor. The size of the disclination, which is proved to be the difference of two sets of su(2)% -like monopoles expressed by two mixed spinors, is quantized topologically in terms of topological invariants$-$winding number. The projection of space-time disclination density along an antisymmetric tensor field is characterized by Brouwer degree and Hopf index.Comment: Revtex, 7 page

Energy-momentum for Randall-Sundrum models

We investigate the conservation law of energy-momentum for Randall-Sundrum models by the general displacement transform. The energy-momentum current has a superpotential and are therefore identically conserved. It is shown that for Randall-Sundrum solution, the momentum vanishes and most of the bulk energy is localized near the Planck brane. The energy density is $\epsilon = \epsilon_0 e^{-3k \mid y \mid}$.Comment: 13 pages, no figures, v4: introduction and new conclusion added, v5: 11 pages, title changed and references added, accepted by Mod. Phys. Lett.

Topological Bose-Mott Insulators in a One-Dimensional Optical Superlattice

We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiments, we show that the topological Chern number can be detected through measuring the density profiles of the bosonic atoms in a harmonic trap.Comment: 5 pages, published versio

Controls and guidance research

The objectives of the control group are concentrated on research and education. The control problem of the hypersonic space vehicle represents an important and challenging issue in aerospace engineering. The work described in this report is part of our effort in developing advanced control strategies for such a system. In order to achieve the objectives stated in the NASA-CORE proposal, the tasks were divided among the group based upon their educational expertise. Within the educational component we are offering a Linear Systems and Control course for students in electrical and mechanical engineering. Also, we are proposing a new course in Digital Control Systems with a corresponding laboratory