A new class of (2+1)(2+1)-d topological superconductor with Z8\mathbb{Z}_8 topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.Comment: 5 pages main text and 3 pages appendix. 1 figur

Scattering on two Aharonov-Bohm vortices with opposite fluxes

The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations

Top-N Recommendation on Graphs

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well-known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.Comment: CIKM 201

A Cosmological Model with Dark Spinor Source

In this paper, we discuss the system of Friedman-Robertson-Walker metric coupling with massive nonlinear dark spinors in detail, where the thermodynamic movement of spinors is also taken into account. The results show that, the nonlinear potential of the spinor field can provide a tiny negative pressure, which resists the Universe to become singular. The solution is oscillating in time and closed in space, which approximately takes the following form g_{\mu\nu}=\bar R^2(1-\delta\cos t)^2\diag(1,-1,-\sin^2r ,-\sin^2r \sin^2\theta), with $\bar R= (1\sim 2)\times 10^{12}$ light year, and $\delta=0.96\sim 0.99$. The present time is about $t\sim 18^\circ$.Comment: 13 pages, no figure, to appear in IJMP

Upper Pseudogap Phase: Magnetic Characterizations

It is proposed that the upper pseudogap phase (UPP) observed in the high-Tc cuprates correspond to the formation of spin singlet pairing under the bosonic resonating-valence-bond (RVB) description. We present a series of evidence in support of such a scenario based on the calculated magnetic properties including uniform spin susceptibility, spin-lattice and spin-echo relaxation rates, which consistently show that strong spin correlations start to develop upon entering the UPP, being enhanced around the momentum (\pi, \pi) while suppressed around (0, 0). The phase diagram in the parameter space of doping concentration, temperature, and external magnetic field, is obtained based on the the bosonic RVB theory. In particular, the competition between the Zeeman splitting and singlet pairing determines a simple relation between the "critical" magnetic field, H_{PG}, and characteristic temperature scale, T0, of the UPP. We also discuss the magnetic behavior in the lower pseudogap phase at a temperature Tv lower than T0, which is characterized by the formation of Cooper pair amplitude where the low-lying spin fluctuations get suppressed at both (0, 0) and (\pi, \pi). Properties of the UPP involving charge channels will be also briefly discussed.Comment: 11 pages, 5 figures, final version to appear in PR