Abstract:
We show that the asymmetric tunneling spectrum observed in the cuprate superconductors stems from the existence of a competing order. The competition between the competing order and superconductivity can create a charge depletion region near the surface. The asymmetric response of the depletion region as the function of the external voltage causes the asymmetric tunneling spectrum. The effect is very general in a system which is near the phase boundary of two competing states favoring different carrier densities. The asymmetry which has recently been observed in the point-contact spectroscopy of the heavy fermion superconductor CeCoIn5 is another example of this effect.

Abstract:
A neighbour-based coordination scheme is proposed for a multi-agent system with multiple leaders. Under assumptions of the connectivity of the interconnection topology and a simple first-order dynamics model for each mobile agent, the results show that all the agents will flock to the polytope region formed by the leaders.

Abstract:
The spin 3/2 fermion models with contact interactions have a {\it generic} SO(5) symmetry without any fine-tuning of parameters. Its physical consequences are discussed in both the continuum and lattice models. A Monte-Carlo algorithm free of the sign problem at any doping and lattice topology is designed when the singlet and quintet interactions satisfy $U_0\le U_2\le -{3\over5} U_0 (U_0\le 0)$, thus making it possible to study different competing orders with high numerical accuracy. This model can be accurately realized in ultra-cold atomic systems.

Abstract:
The generic symmetry of a system under a uniform Zeeman magnetic field is U(1) x U(1). However, we show that SO(5) models in the presence of a finite chemical potential and a finite Zeeman magnetic field can have a exact SU(2) x U(1) symmetry. This principle can be used to test SO(5) symmetry at any doping level.

Abstract:
According to Wilson's theory of critical phenomena, critical exponents are universal functions of $d$, the dimension of space, and $n$, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where $T_N$ and $T_c$ intersect. By measuring critical exponents close to the bicritical point, and knowing that $d=3$, one can experimentally measure the number 5 of the SO(5) theory.

Abstract:
A key prediction of the SO(5) theory is the antiferromagnetic vortex state. Recent neutron scattering experiment on LSCO superconductors revealed enhanced antiferromagnetic order in the vortex state. Here we review theoretical progress since the original proposal and present a theory of static and dynamic antiferromanetic vortices in LSCO superconductors. It is shown that the antiferromagnetic region induced by the vortices can be greater than the coherence length, due to the light effective mass of the dynamic antiferromagnetic fluctuations at optimal doping, and close promixity to the antiferromagentic state in the underdoped regime. Systematic experiments are proposed to unambiguously determine that the field induced magnetic scattering originates from the vortices and not from the bulk.

Abstract:
This paper is concerned with a leader-following consensus problem for networks of agents with fixed and switching topologies as well as nonuniform time-varying communication delays. By employing Lyapunov-Razumikhin function, a necessary and sufficient condition is derived in the case of fixed topology, and a sufficient condition is obtained in the case when the interconnection topology is switched and satisfies certain condition. Simulation results are provided to illustrate the theoretical results.

Abstract:
Molecules of the title compound, C56H76Cl4O16S4, have crystallographic C2 symmetry and adopt a 1,3-alternate conformation where the four –OCH2CH2OCH2CH2Cl groups are located alternately above and below the virtual plane (R) defined by the four bridging S atoms. The dihedral angles between the plane (R) and the phenolic rings are 72.85 (7) and 74.57 (7)°. An unusual 24-membered macrocyclic ring is formed in the crystal structure with an array of eight intramolecular C—H...O hydrogen bonds between the ether arm H atoms and the sulfonyl O atoms. In the supramolecular structure, the molecular components are linked into infinite zigzag one-dimensional chains by a combination of four intermolecular C—H...O hydrogen bonds, forming R22(13), R22(16), R22(21) and R22(26) ring motifs. These chains are augmented into a wave-like two-dimensional network by weak C...O interactions. One tert-butyl group shows rotational disorder, and one CH2CH2Cl group is disordered over two orientations; the site-occupation factors are 0.756 (6) and 0.244 (6) for the two tert-butyl groups, and 0.808 (3) and 0.192 (3) for the two CH2CH2Cl units.

Abstract:
We construct a class of projected SO(5) models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO(5) symmetry where all static correlation functions are exactly SO(5) symmetric and discuss the signature of the projected SO(5) symmetry in dynamical correlation functions. We show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high T_c superconductors and account for many of their physical properties.

Abstract:
We investigate the conductivity $\sigma$ of graphene nanoribbons with zigzag edges as a function of Fermi energy $E_F$ in the presence of the impurities with different potential range. The dependence of $\sigma(E_F)$ displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of $\sigma(E_F)$ and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao \emph{et al.} (to appear in Science).