2,453 research outputs found
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
meson effects on neutron stars in the modified quark-meson coupling model
The properties of neutron stars are investigated by including meson
field in the Lagrangian density of modified quark-meson coupling model. The
population with meson is larger than that without
meson at the beginning, but it becomes smaller than that without meson
as the appearance of . The 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
meson effects. The meson increases the maximum masses of
neutron stars. The influence of on the meson effects
are also investigated.Comment: 10 pages, 6 figures, 4 table
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