Domain walls in gapped graphene

The electronic properties of a particular class of domain walls in gapped graphene are investigated. We show that they can support mid-gap states which are localized in the vicinity of the domain wall and propagate along its length. With a finite density of domain walls, these states can alter the electronic properties of gapped graphene significantly. If the mid-gap band is partially filled,the domain wall can behave like a one-dimensional metal embedded in a semi-conductor, and could potentially be used as a single-channel quantum wire.Comment: 4 pgs. revte

Symplectic Geometry on Quantum Plane

A study of symplectic forms associated with two dimensional quantum planes and the quantum sphere in a three dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit.Comment: 12 pages, Late

Gravitino dark matter from gluino late decay in split supersymmetry

In split-supersymmetry (split-SUSY), gluino is a metastable particle and thus can freeze out in the early universe. The late decay of such a long-life gluino into the lightest supersymmetric particle (LSP) may provide much of the cosmic dark matter content. In this work, assuming the LSP is gravitino produced from the late decay of the metastable gluino, we examine the WMAP dark matter constraints on the gluino mass. We find that to provide the full abundance of dark matter, the gluino must be heavier than about 14 TeV and thus not accessible at the CERN Large Hadron Collider (LHC).Comment: discussions added (version in PRD

BRST Structures and Symplectic Geometry on a Class of Supermanifolds

By investigating the symplectic geometry and geometric quantization on a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed and q-deformed cases in the classical as well as in the quantum cases.Comment: 14 pages, Late

Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.Comment: 43 pages; 2 figures; To be published in Advances in Mathematics (2019