683 research outputs found
On kernel engineering via Paley–Wiener
A radial basis function approximation takes the form
where the coefficients a 1,…,a n are real numbers, the centres b 1,…,b n are distinct points in ℝ d , and the function φ:ℝ d →ℝ is radially symmetric. Such functions are highly useful in practice and enjoy many beautiful theoretical properties. In particular, much work has been devoted to the polyharmonic radial basis functions, for which φ is the fundamental solution of some iterate of the Laplacian. In this note, we consider the construction of a rotation-invariant signed (Borel) measure μ for which the convolution ψ=μ φ is a function of compact support, and when φ is polyharmonic. The novelty of this construction is its use of the Paley–Wiener theorem to identify compact support via analysis of the Fourier transform of the new kernel ψ, so providing a new form of kernel engineering
Quantum tunneling through planar p-n junctions in HgTe quantum wells
We demonstrate that a p-n junction created electrically in HgTe quantum wells
with inverted band-structure exhibits interesting intraband and interband
tunneling processes. We find a perfect intraband transmission for electrons
injected perpendicularly to the interface of the p-n junction. The opacity and
transparency of electrons through the p-n junction can be tuned by changing the
incidence angle, the Fermi energy and the strength of the Rashba spin-orbit
interaction. The occurrence of a conductance plateau due to the formation of
topological edge states in a quasi-one-dimensional p-n junction can be switched
on and off by tuning the gate voltage. The spin orientation can be
substantially rotated when the samples exhibit a moderately strong Rashba
spin-orbit interaction.Comment: 4 pages, 4 figure
Low-field diffusion magneto-thermopower of a high mobility two-dimensional electron gas
The low magnetic field diffusion thermopower of a high mobility
GaAs-heterostructure has been measured directly on an electrostatically defined
micron-scale Hall-bar structure at low temperature (T = 1.6 K) in the low
magnetic field regime (B < 1.2 T) where delocalized quantum Hall states do not
influence the measurements. The sample design allowed the determination of the
field dependence of the thermopower both parallel and perpendicular to the
temperature gradient, denoted respectively by Sxx (longitudinal thermopower)
and Syx (Nernst-Ettinghausen coefficient). The experimental data show clear
oscillations in Sxx and Syx due to the formation of Landau levels for 0.3 T < B
< 1.2 T and reveal that Syx is approximately 120 times larger than Sxx at a
magnetic field of 1 T, which agrees well with the theoretical prediction.Comment: 4 pages, 4 figure
Casimir force on amplifying bodies
Based on a unified approach to macroscopic QED that allows for the inclusion
of amplification in a limited space and frequency range, we study the Casimir
force as a Lorentz force on an arbitrary partially amplifying system of
linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate
that the force on a weakly polarisable/magnetisable amplifying object in the
presence of a purely absorbing environment can be expressed as a sum over the
Casimir--Polder forces on the excited atoms inside the body. As an example, the
resonant force between a plate consisting of a dilute gas of excited atoms and
a perfect mirror is calculated
Van-der-Waals potentials of paramagnetic atoms
We study single- and two-atom van der Waals interactions of ground-state
atoms which are both polarizable and paramagnetizable in the presence of
magneto-electric bodies within the framework of macroscopic quantum
electrodynamics. Starting from an interaction Hamiltonian that includes
particle spins, we use leading-order perturbation theory for the van der Waals
potentials expressed in terms of the polarizability and magnetizability of the
atom(s). To allow for atoms embedded in media, we also include local-field
corrections via the real-cavity model. The general theory is applied to the
potential of a single atom near a half space and that of two atoms embedded in
a bulk medium or placed near a sphere, respectively.Comment: 18 pages, 3 figures, 1 tabl
An Anderson-Fano Resonance and Shake-Up Processes in the Magneto-Photoluminescence of a Two-Dimensional Electron System
We report an anomalous doublet structure and low-energy satellite in the
magneto-photoluminescence spectra of a two-dimensional electron system. The
doublet structure moves to higher energy with increasing magnetic field and is
most prominent at odd filling factors 5 and 3. The lower-energy satellite peak
tunes to lower energy for increasing magnetic field between filling factor 6
and 2. These features occur at energies below the fundamental band of
recombination originating from the lowest Landau level and display striking
magnetic field and temperature dependence that indicates a many-body origin.
Drawing on a recent theoretical description of Hawrylak and Potemski, we show
that distinct mechanisms are responsible for each feature.Comment: 14 pages including 5 figures. To appear in the April 15th edition of
Phy. Rev. B. rapid com
Counting approximately-shortest paths in directed acyclic graphs
Given a directed acyclic graph with positive edge-weights, two vertices s and
t, and a threshold-weight L, we present a fully-polynomial time
approximation-scheme for the problem of counting the s-t paths of length at
most L. We extend the algorithm for the case of two (or more) instances of the
same problem. That is, given two graphs that have the same vertices and edges
and differ only in edge-weights, and given two threshold-weights L_1 and L_2,
we show how to approximately count the s-t paths that have length at most L_1
in the first graph and length at most L_2 in the second graph. We believe that
our algorithms should find application in counting approximate solutions of
related optimization problems, where finding an (optimum) solution can be
reduced to the computation of a shortest path in a purpose-built auxiliary
graph
Nonlocal edge state transport in the quantum spin Hall state
We present direct experimental evidence for nonlocal transport in HgTe
quantum wells in the quantum spin Hall regime, in the absence of any external
magnetic field. The data conclusively show that the non-dissipative quantum
transport occurs through edge channels, while the contacts lead to
equilibration between the counter-propagating spin states at the edge. We show
that the experimental data agree quantitatively with the theory of the quantum
spin Hall effect.Comment: 13 pages, 4 figure
- …