3,215 research outputs found
Connected Spatial Networks over Random Points and a Route-Length Statistic
We review mathematically tractable models for connected networks on random
points in the plane, emphasizing the class of proximity graphs which deserves
to be better known to applied probabilists and statisticians. We introduce and
motivate a particular statistic measuring shortness of routes in a network.
We illustrate, via Monte Carlo in part, the trade-off between normalized
network length and in a one-parameter family of proximity graphs. How close
this family comes to the optimal trade-off over all possible networks remains
an intriguing open question. The paper is a write-up of a talk developed by the
first author during 2007--2009.Comment: Published in at http://dx.doi.org/10.1214/10-STS335 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Modeling the reconstructed BAO in Fourier space
The density field reconstruction technique, which was developed to partially
reverse the nonlinear degradation of the Baryon Acoustic Oscillation (BAO)
feature in the galaxy redshift surveys, has been successful in substantially
improving the cosmology constraints from recent galaxy surveys such as Baryon
Oscillation Spectroscopic Survey (BOSS). We estimate the efficiency of the
reconstruction method as a function of various reconstruction details. To
directly quantify the BAO information in nonlinear density fields before and
after reconstruction, we calculate the cross-correlations (i.e., propagators)
of the pre(post)-reconstructed density field with the initial linear field
using a mock galaxy sample that is designed to mimic the clustering of the BOSS
CMASS galaxies. The results directly provide the BAO damping as a function of
wavenumber that can be implemented into the Fisher matrix analysis. We focus on
investigating the dependence of the propagator on a choice of smoothing filters
and on two major different conventions of the redshift-space density field
reconstruction that have been used in literature. By estimating the BAO
signal-to-noise for each case, we predict constraints on the angular diameter
distance and Hubble parameter using the Fisher matrix analysis. We thus
determine an optimal Gaussian smoothing filter scale for the signal-to-noise
level of the BOSS CMASS. We also present appropriate BAO fitting models for
different reconstruction methods based on the first and second order Lagrangian
perturbation theory in Fourier space. Using the mock data, we show that the
modified BAO fitting model can substantially improve the accuracy of the BAO
position in the best fits as well as the goodness of the fits.Comment: 21 pages, 7 figures, 1 table. Minor revisions. Matches version
accepted by MNRA
Transverse electric current induced by optically injected spin current in cross-shaped InGaAs/InAlAs system
We examine electric response of a linearly polarized light normally shed on a
cross-shaped quasi 2-dimensional InGaAs/InAlAs system with structure inversion
asymmetry. The photo-excited conduction electrons carry a pure spin current
with in-plane spin polarization due to the Rashba spin-orbit interaction. We
use Landauer-B\"{u}ttiker formalism to show that this spin current induces two
inward or outward transverse charge currents, which are observable in
experiments. This effect may serve as an experimental probe of certain types of
spin current.Comment: 5 pages, 3 figure
Topological Anderson Insulator
Disorder plays an important role in two dimensions, and is responsible for
striking phenomena such as metal insulator transition and the integral and
fractional quantum Hall effects. In this paper, we investigate the role of
disorder in the context of the recently discovered topological insulator, which
possesses a pair of helical edge states with opposing spins moving in opposite
directions and exhibits the phenomenon of quantum spin Hall effect. We predict
an unexpected and nontrivial quantum phase termed "topological Anderson
insulator," which is obtained by introducing impurities in a two-dimensional
metal; here disorder not only causes metal insulator transition, as
anticipated, but is fundamentally responsible for creating extended edge
states. We determine the phase diagram of the topological Anderson insulator
and outline its experimental consequences.Comment: 4 pages, 4 figure
Spin resolved Hall effect driven by spin-orbit coupling
Spin and electric Hall currents are calculated numerically in a
two-dimensional mesoscopic system with Rashba and Dresselhaus spin-orbit
coupling by means of the Landauer-Buttiker formalism. It is found that both
electric and spin Hall currents circulate when two spin-orbit couplings
coexist, while the electric Hall conductance vanishes if either one is absent.
The electric and spin Hall conductances are suppressed in strong disorder, but
survive in weak disorder. Physically it can be understood that the spinomotive
transverse "force" generated by spin-orbit coupling is responsible for the
formation of the spin Hall current and the lack of transverse reflection
symmetry is the origin of the electric Hall current.Comment: 4 pages, 5 figure
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