20,109 research outputs found
Deformations of Annuli on Riemann surfaces with Smallest Mean Distortion
Let and be two circular annuli and let be a radial metric
defined in the annulus . Consider the class of
harmonic mappings between and . It is proved recently by
Iwaniec, Kovalev and Onninen that, if (i.e. if is Euclidean
metric) then is not empty if and only if there holds the
Nitsche condition (and thus is proved the J. C. C. Nitsche conjecture). In this
paper we formulate an condition (which we call Nitsche conjecture) with
corresponds to and define Nitsche harmonic maps. We
determine the extremal mappings with smallest mean distortion for mappings of
annuli w.r. to the metric . As a corollary, we find that Nitsche
harmonic maps are Dirichlet minimizers among all homeomorphisms .
However, outside the -Nitsche condition of the modulus of the annuli,
within the class of homeomorphisms, no such energy minimizers exist. % However,
%outside the Nitsche range of the modulus of the annuli, %within the
class of homeomorphisms, no such energy minimizers exist. This extends some
recent results of Astala, Iwaniec and Martin (ARMA, 2010) where it is
considered the case and .Comment: Some misprints are corrected in this version (see Lemma~5.1
Common Codebook Millimeter Wave Beam Design: Designing Beams for Both Sounding and Communication with Uniform Planar Arrays
Fifth generation (5G) wireless networks are expected to utilize wide
bandwidths available at millimeter wave (mmWave) frequencies for enhancing
system throughput. However, the unfavorable channel conditions of mmWave links,
e.g., higher path loss and attenuation due to atmospheric gases or water vapor,
hinder reliable communications. To compensate for these severe losses, it is
essential to have a multitude of antennas to generate sharp and strong beams
for directional transmission. In this paper, we consider mmWave systems using
uniform planar array (UPA) antennas, which effectively place more antennas on a
two-dimensional grid. A hybrid beamforming setup is also considered to generate
beams by combining a multitude of antennas using only a few radio frequency
chains. We focus on designing a set of transmit beamformers generating beams
adapted to the directional characteristics of mmWave links assuming a UPA and
hybrid beamforming. We first define ideal beam patterns for UPA structures.
Each beamformer is constructed to minimize the mean squared error from the
corresponding ideal beam pattern. Simulation results verify that the proposed
codebooks enhance beamforming reliability and data rate in mmWave systems.Comment: 14 pages, 10 figure
Strongly modulated transmission of a spin-split quantum wire with local Rashba interaction
We investigate the transport properties of ballistic quantum wires in the
presence of Zeeman spin splittings and a spatially inhomogeneous Rashba
interaction. The Zeeman interaction is extended along the wire and produces
gaps in the energy spectrum which allow electron propagation only for spinors
lying along a certain direction. For spins in the opposite direction the waves
are evanescent far away from the Rashba region, which plays the role of the
scattering center. The most interesting case occurs when the magnetic field is
perpendicular to the Rashba field. Then, the spins of the asymptotic
wavefunctions are not eigenfunctions of the Rashba Hamiltonian and the
resulting coupling between spins in the Rashba region gives rise to sudden
changes of the transmission probability when the Fermi energy is swept along
the gap. After briefly examining the energy spectrum and eigenfunctions of a
wire with extended Rashba coupling, we analyze the transmission through a
region of localized Rashba interaction, in which a double interface separates a
region of constant Rashba interaction from wire leads free from spin-orbit
coupling. For energies slightly above the propagation threshold, we find the
ubiquitous occurrence of transmission zeros (antiresonances) which are analyzed
by matching methods in the one-dimensional limit. We find that a a minimal
tight-binding model yields analytical transmission lineshapes of Fano
antiresonance type. More general angular dependences of the external magnetic
field is treated within projected Schroedinger equations with Hamiltonian
matrix elements mixing wavefunction components. Finally, we consider a
realistic quantum wire where the energy subbands are coupled via the Rashba
intersubband coupling term and discuss its effect on the transmission zeros.Comment: 11 pages, 12 figure
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