121,914 research outputs found
Tall sections from non-minimal transformations
In previous work, we have shown that elliptic fibrations with two sections,
or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass
model of a certain form, namely, the Jacobian of a model.
Most constructions of elliptically fibered Calabi-Yau manifolds with two
sections have been carried out assuming that the image of this birational map
was a "minimal" Weierstrass model. In this paper, we show that for some
elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the
Jacobian of the model is not minimal. Said another way,
starting from a Calabi-Yau Weierstrass model, the total space must be blown up
(thereby destroying the "Calabi-Yau" property) in order to embed the model into
. In particular, we show that the elliptic fibrations studied
recently by Klevers and Taylor fall into this class of models.Comment: 16 page
States near Dirac points of rectangular graphene dot in a magnetic field
In neutral graphene dots the Fermi level coincides with the Dirac points. We
have investigated in the presence of a magnetic field several unusual
properties of single electron states near the Fermi level of such a
rectangular-shaped graphene dot with two zigzag and two armchair edges. We find
that a quasi-degenerate level forms near zero energy and the number of states
in this level can be tuned by the magnetic field. The wavefunctions of states
in this level are all peaked on the zigzag edges with or without some weight
inside the dot. Some of these states are magnetic field-independent surface
states while the others are field-dependent. We have found a scaling result
from which the number of magnetic field-dependent states of large dots can be
inferred from those of smaller dots.Comment: Physical review B in pres
Comment on "Fock-Darwin States of Dirac Electrons in Graphene-Based Artificial Atoms"
Chen, Apalkov, and Chakraborty (Phys. Rev. Lett. 98, 186803 (2007)) have
computed Fock-Darwin levels of a graphene dot by including only basis states
with energies larger than or equal to zero. We show that their results violate
the Hellman-Feynman theorem. A correct treatment must include both positive and
negative energy basis states. Additional basis states lead to new energy levels
in the optical spectrum and anticrossings between optical transition lines.Comment: 1 page, 1 figure, accepted for publication in PR
Remark on the effective potential of the gravitational perturbation in the black hole background projected on the brane
The polar perturbation is examined when the spacetime is expressed by a 4d
metric induced from higher-dimensional Schwarzschild geometry. Since the
spacetime background is not a vacuum solution of 4d Einstein equation, the
various general principles are used to understand the behavior of the
energy-momentum tensor under the perturbation. It is found that although the
general principles fix many components, they cannot fix two components of the
energy-momentum tensor. Choosing two components suitably, we derive the
effective potential which has a correct 4d limit.Comment: 12 pages, no figure, CQG accepte
Characterization of low-energy magnetic excitations in chromium
The low-energy excitations of Cr, i.e. the Fincher-Burke (FB) modes, have
been investigated in the transversely polarized spin-density-wave phase by
inelastic neutron scattering using a single-(Q+-) crystal with a propagation
vector (Q+-) parallel to [0,0,1]. The constant-momentum-transfer scans show
that the energy spectra consist of two components, namely dispersive FB modes
and an almost energy-independent cross section. Most remarkably, we find that
the spectrum of the FB modes exhibits one peak at 140 K near Q = (0,0,0.98) and
two peaks near Q = (0,0,1.02), respectively. This is surprising because Cr
crystallizes in a centro-symmetric bcc structure. The asymmetry of those energy
spectra decreases with increasing temperature. In addition, the observed
magnetic peak intensity is independent of Q suggesting a transfer of
spectral-weight between the upper and lower FB modes. The energy-independent
cross section is localized only between the incommensurate peaks and develops
rapidly with increasing temperature.Comment: 6 pages, 8 figure
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