2,528 research outputs found
A glimpse of the conformal structure of random planar maps
We present a way to study the conformal structure of random planar maps. The
main idea is to explore the map along an SLE (Schramm--Loewner evolution)
process of parameter and to combine the locality property of the
SLE_{6} together with the spatial Markov property of the underlying lattice in
order to get a non-trivial geometric information. We follow this path in the
case of the conformal structure of random triangulations with a boundary. Under
a reasonable assumption called (*) that we have unfortunately not been able to
verify, we prove that the limit of uniformized random planar triangulations has
a fractal boundary measure of Hausdorff dimension almost surely.
This agrees with the physics KPZ predictions and represents a first step
towards a rigorous understanding of the links between random planar maps and
the Gaussian free field (GFF).Comment: To appear in Commun. Math. Phy
Atomic-Layer-Deposited Al2O3 on Bi2Te3 for Topological Insulator Field-Effect Transistors
We report dual-gate modulation of topological insulator field-effect
transistors (TI FETs) made on Bi2Te3 thin flakes with integration of
atomic-layer-deposited (ALD) Al2O3 high-k dielectric. Atomic force microscopy
study shows that ALD Al2O3 is uniformly grown on this layer-structured channel
material. Electrical characterization reveals that the right selection of ALD
precursors and the related surface chemistry play a critical role in device
performance of Bi2Te3 based TI FETs. We realize both top-gate and bottom-gate
control on these devices, and the highest modulation rate of 76.1% is achieved
by using simultaneous dual gate control.Comment: 4 pages, 3 figure
Bondi mass with a cosmological constant
The mass loss of an isolated gravitating system due to energy carried away by
gravitational waves with a cosmological constant was recently
worked out, using the Newman-Penrose-Unti approach. In that same article, an
expression for the Bondi mass of the isolated system, , for the
case was proposed. The stipulated mass would ensure
that in the absence of any incoming gravitational radiation from elsewhere, the
emitted gravitational waves must carry away a positive-definite energy. That
suggested quantity however, introduced a -correction term to the Bondi
mass (where is the usual Bondi mass for asymptotically flat
spacetimes) which would involve not just information on the state of the system
at that moment, but ostensibly also its past history. In this paper, we derive
the identical mass-loss equation using an integral formula on a hypersurface
formulated by Frauendiener based on the Nester-Witten identity, and argue that
one may adopt a generalisation of the Bondi mass with
\emph{without any correction}, viz. for any .
Furthermore with , we show that for \emph{purely quadrupole
gravitational waves} given off by the isolated system (i.e. when the "Bondi
news" comprises only the components of the "spherical
harmonics with spin-weight 2"), the energy carried away is \emph{manifestly
positive-definite} for the case. For a general having
higher multipole moments, this perspicuous property in the case
still holds if those contributions are weak --- more precisely, if they
satisfy any of the inequalities given in this paper.Comment: 29 pages, accepted for publication by Physical Review
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