Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Giant mesoscopic spin Hall effect on surface of topological insulator

We study mesoscopic spin Hall effect on the surface of topological insulator with a step-function potential. The giant spin polarization induced by a transverse electric current is derived analytically by using McMillan method in the ballistic transport limit, which oscillates across the potential boundary with no confinement from the potential barrier due to the Klein paradox, and should be observable in spin resolved scanning tunneling microscope.Comment: 5 pages, 3 figure

Half Metallic Bilayer Graphene

Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers have same magnitude with opposite directions. We propose that lightly charged bilayer graphene in an electric field perpendicular to the graphene plane may be a half metal as a consequence of the inversion and particle-hole symmetry broken in the LAF state. We show this explicitly by using a mean field theory on a 2-layer Hubbard model for the bilayer graphene.Comment: 4+ pages, 4 figure

δ\delta meson effects on neutron stars in the modified quark-meson coupling model

The properties of neutron stars are investigated by including $\delta$ meson field in the Lagrangian density of modified quark-meson coupling model. The $\Sigma^-$ population with $\delta$ meson is larger than that without $\delta$ meson at the beginning, but it becomes smaller than that without $\delta$ meson as the appearance of $\Xi^-$. The $\delta$ meson has opposite effects on hadronic matter with or without hyperons: it softens the EOSes of hadronic matter with hyperons, while it stiffens the EOSes of pure nucleonic matter. Furthermore, the leptons and the hyperons have the similar influence on $\delta$ meson effects. The $\delta$ meson increases the maximum masses of neutron stars. The influence of $(\sigma^*,\phi)$ on the $\delta$ meson effects are also investigated.Comment: 10 pages, 6 figures, 4 table