531 research outputs found
A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials
We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and
Topological Materials), a library and code generator based on a domain-specific
language tailored to implement the specific stencil-like algorithms that can
describe Dirac and topological materials such as graphene and topological
insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP)
code is fully vectorized using Single Instruction Multiple Data (SIMD)
extensions. It is significantly faster than matrix-based approaches on the node
level and performs in accordance with the roofline model. We demonstrate the
chip-level performance and distributed-memory scalability of basic building
blocks such as sparse matrix-(multiple-) vector multiplication on modern
multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i)
explore the scattering of a Dirac wave on an array of gate-defined quantum
dots, to (ii) calculate a bunch of interior eigenvalues for strong topological
insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl
semimetal.Comment: 16 pages, 2 tables, 11 figure
Deformable kernels for early vision
Early vision algorithms often have a first stage of linear filtering
that 'extracts' from the image information at multiple
scales of resolution and multiple orientations. A common
difficulty in the design and implementation of such
schemes is that one feels compelled to discretize coarsely
the space of scales and orientations in order to reduce computation and storage costs. This discretization produces
anisotropies due to a loss of traslation-, rotation- scaling- invariance that makes early vision algorithms less precise and
more difficult to design. This need not be so: one can compute
and store efficiently the response of families of linear
filters defined on a continuum of orientations and scales. A
technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of
a small number of 'basis' functions; (2) to describe all finite-dimensional families, i.e. the families of filters for which a
finite dimensional representation is possible with no error.
The technique is general and can be applied to generating
filters in arbitrary dimensions. Experimental results are presented that demonstrate the applicability of the technique to
generating multi-orientation multi-scale 20 edge-detection
kernels. The implementation issues are also discussed
Synergies between radio, optical and microwave observations at high redshift
We study synergies between three promising methods to measure
large-scale structure in the next decade. Optical spectroscopic surveys are the
most mature, but become increasingly difficult at and suffer from
interloper problems even for spectroscopic surveys. Intensity mapping of the
21-cm signal can cover large volumes with exquisite fidelity, but is limited
both by loss of information to foreground cleaning and by lack of knowledge of
the mean signal. Cosmic microwave background (CMB) lensing is theoretically
very clean, but ultimately measures just the projected variations in density.
We find that cross-correlation between optical and radio can significantly
improve the measurement of growth rate. Combining these with the CMB provides a
promising avenue to detecting modified gravity at high redshifts, in particular
by independently probing the Weyl and Newtonian potentials and by strengthening
control of systematics. We find that cross-correlating a Stage {\sc ii} 21-cm
survey with DESI quasars with a reasonable brightness temperature prior could
enable measurements of the growth rate at sub 3\% and sub 8\%
levels at , representing a factor of 4 and 8 improvement over
constraints obtainable from DESI quasars alone. Similarly, cross-correlating
21-cm data with a futuristic LBG survey to over 1000 square
degrees will make possible measurements at close to 1\% at
and 3\% at , and improve similar constraints at by close to a
factor of 3 to sub-10\% precision. Combining the above with CMB lensing from a
Stage 4 CMB survey and LSST data can additionally constrain the gravitational
slip parameter to similar precision at these redshifts, enabling us to
test the predictions of general relativity at large scales.Comment: Updated to match version accepted by JCAP. Fixed typo in Equation
3.2, updated 21-cm experiment specifications and added Figure
Topological Photonics
Topological photonics is a rapidly emerging field of research in which
geometrical and topological ideas are exploited to design and control the
behavior of light. Drawing inspiration from the discovery of the quantum Hall
effects and topological insulators in condensed matter, recent advances have
shown how to engineer analogous effects also for photons, leading to remarkable
phenomena such as the robust unidirectional propagation of light, which hold
great promise for applications. Thanks to the flexibility and diversity of
photonics systems, this field is also opening up new opportunities to realize
exotic topological models and to probe and exploit topological effects in new
ways. This article reviews experimental and theoretical developments in
topological photonics across a wide range of experimental platforms, including
photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon
photonics, and circuit QED. A discussion of how changing the dimensionality and
symmetries of photonics systems has allowed for the realization of different
topological phases is offered, and progress in understanding the interplay of
topology with non-Hermitian effects, such as dissipation, is reviewed. As an
exciting perspective, topological photonics can be combined with optical
nonlinearities, leading toward new collective phenomena and novel strongly
correlated states of light, such as an analog of the fractional quantum Hall
effect.Comment: 87 pages, 30 figures, published versio
Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs
While all media can exhibit first-order conductivity describing current
linearly proportional to electric field, , the second-order conductivity,
, relating current to , is nonzero only when inversion
symmetry is broken. Second order nonlinear optical responses are powerful tools
in basic research, as probes of symmetry breaking, and in optical technology as
the basis for generating currents from far-infrared to X-ray wavelengths. The
recent surge of interest in Weyl semimetals with acentric crystal structures
has led to the discovery of a host of -related phenomena in this
class of materials, such as polarization-selective conversion of light to dc
current (photogalvanic effects) and the observation of giant second-harmonic
generation (SHG) efficiency in TaAs at photon energy 1.5 eV. Here, we present
measurements of the SHG spectrum of TaAs revealing that the response at 1.5 eV
corresponds to the high-energy tail of a resonance at 0.7 eV, at which point
the second harmonic conductivity is approximately 200 times larger than seen in
the standard candle nonlinear crystal, GaAs. This remarkably large SHG response
provokes the question of ultimate limits on , which we address
by a new theorem relating frequency-integrated nonlinear response functions to
the third cumulant (or "skewness") of the polarization distribution function in
the ground state. This theorem provides considerable insight into the factors
that lead to the largest possible second-order nonlinear response, specifically
showing that the spectral weight is unbounded and potentially divergent when
the possibility of next-neighbor hopping is included.Comment: 7 pages, 4 figure
- …