26,925 research outputs found
Fitting functions for dark matter density profiles
We present a unified parameterization of the fitting functions suitable for
density profiles of dark matter haloes or elliptical galaxies. A notable
feature is that the classical Einasto profile appears naturally as the
continuous limiting case of the cored subfamily amongst the double power-law
profiles of Zhao (1996). Based on this, we also argue that there is basically
no qualitative difference between halo models well-fitted by the Einasto
profile and the standard NFW model. This may even be the case quantitatively
unless the resolutions of simulations and the precisions of fittings are
sufficiently high to make meaningful distinction possible.Comment: 13 pages (6 pages main text + 5 pages appendices + 2 pages full
tables) including 5 figures and 7 tables. submitted to MNRA
A Geometric Definition Of Schubert Polynomials and Dual Schubert Polynomials For Classical Lie Groups
In this paper, we first discuss the topological properties of projective
Stiefel manifolds, we compute their cohomology rings and classify their
cohomology endomorphisms; Then by embedding the flag manifold of a classical
Lie group into its corresponding infinite dimensional projective Stiefel
manifold(which is homotopic to the product of infinite dimensional complex
projective space ), we define the Schubert polynomials
and dual Schubert polynomials. Finally we discuss the property and the
computation of these polynomials.Comment: This paper has been withdrawn by the author due to a crucial This
paper have a vital error in Lemma 2.1. So the definition for Schubert
polynomials are not valid for Lie groups of type B,C,
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
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