NP-Logic Systems and Model-Equivalence Reductions

In this paper we investigate the existence of model-equivalence reduction between NP-logic systems which are logic systems with model existence problem in NP. It is shown that among all NP-systems with model checking problem in NP, the existentially quantified propositional logic (\exists PF) is maximal with respect to poly-time model-equivalent reduction. However, \exists PF seems not a maximal NP-system in general because there exits a NP-system with model checking problem D^P-complete

The Vertical X-shaped Structure in the Milky Way: Evidence from a Simple Boxy Bulge Model

A vertical X-shaped structure was recently reported in the Galactic bulge. Here we present evidence of a similar X-shaped structure in the Shen et al. (2010) bar/boxy bulge model that simultaneously matches the stellar kinematics successfully. The X-shaped structure is found in the central region of our bar/boxy bulge model, and is qualitatively consistent with the observed one in many aspects. End-to-end separations of the X-shaped structure in the radial and vertical directions are roughly 3 kpc and 1.8 kpc, respectively. The X-shaped structure contains about 7% of light in the boxy bulge region, but it is significant enough to be identified in observations. An X-shaped structure naturally arises in the formation of bar/boxy bulges, and is mainly associated with orbits trapped around the vertically-extended x_1 family. Like the bar in our model, the X-shaped structure tilts away from the Sun--Galactic center line by 20 degrees. The X-shaped structure becomes increasingly symmetric about the disk plane, so the observed symmetry may indicate that it formed at least a few billion years ago. The existence of the vertical X-shaped structure suggests that the formation of the Milky Way bulge is shaped mainly by internal disk dynamical instabilities.Comment: Accepted for publication in ApJL; minor changes after the referee's report; 6 pages; emulateapj forma

Quantum Anomalous Hall Effect in Flat Band Ferromagnet

We proposed a theory of quantum anomalous Hall effect in a flat-band ferromagnet on a two-dimensional (2D) decorated lattice with spin-orbit coupling. Free electrons on the lattice have dispersionless flat bands, and the ground state is highly degenerate when each lattice site is occupied averagely by one electron, i.e., the system is at half filling. The on-site Coulomb interaction can remove the degeneracy and give rise to the ferrimagnetism, which is the coexistence of the ferromagnetic and antiferromagnetic long-range orders. On the other hand the spin-orbit coupling makes the band structure topologically non-trivial, and produces the quantum spin Hall effect with a pair of helical edge states around the system boundary. Based on the rigorous results for the Hubbard model, we found that the Coulomb interaction can provide an effective staggered potential and turn the quantum spin Hall phase into a quantum anomalous Hall phase

Theoretical Models of the Galactic Bulge

Near infrared images from the COBE satellite presented the first clear evidence that our Milky Way galaxy contains a boxy shaped bulge. Recent years have witnessed a gradual paradigm shift in the formation and evolution of the Galactic bulge. Bulges were commonly believed to form in the dynamical violence of galaxy mergers. However, it has become increasingly clear that the main body of the Milky Way bulge is not a classical bulge made by previous major mergers, instead it appears to be a bar seen somewhat end-on. The Milky Way bar can form naturally from a precursor disk and thicken vertically by the internal firehose/buckling instability, giving rise to the boxy appearance. This picture is supported by many lines of evidence, including the asymmetric parallelogram shape, the strong cylindrical rotation (i.e., nearly constant rotation regardless of the height above the disk plane), the existence of an intriguing X-shaped structure in the bulge, and perhaps the metallicity gradients. We review the major theoretical models and techniques to understand the Milky Way bulge. Despite the progresses in recent theoretical attempts, a complete bulge formation model that explains the full kinematics and metallicity distribution is still not fully understood. Upcoming large surveys are expected to shed new light on the formation history of the Galactic bulge.Comment: Invited review to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing, 2015, in press. 27 pages, 7 figure

Scattering theory for subcritical wave equation with inverse square potential

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method of [37], [38] and [41], we establish energy flux estimates on the light cone. Then by the characteristic line method and radiation theorem, we show the radial energy solutions scatter to free waves outside the light cone. Moreover, by extending the Morawetz estimates, we prove scattering theory for the solutions with initial datum in the weighted energy spaces.Comment: Minor change