6,619 research outputs found
Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials
We study the two-point correlation functions for the zeroes of systems of
-invariant Gaussian random polynomials on and systems
of -invariant Gaussian analytic functions. Our result
reflects the same "repelling," "neutral," and "attracting" short-distance
asymptotic behavior, depending on the dimension, as was discovered in the
complex case by Bleher, Shiffman, and Zelditch. For systems of the -invariant Gaussian analytic functions we also obtain a
fast decay of correlations at long distances.
We then prove that the correlation function for the -invariant Gaussian analytic functions is "universal,"
describing the scaling limit of the correlation function for the restriction of
systems of the -invariant Gaussian random polynomials to any
-dimensional submanifold . This provides a
real counterpart to the universality results that were proved in the complex
case by Bleher, Shiffman, and Zelditch. (Our techniques also apply to the
complex case, proving a special case of the universality results of Bleher,
Shiffman, and Zelditch.)Comment: 28 pages, 1 figure. To appear in International Mathematics Research
Notices (IMRN
Enhanced Efficiency of Light-Trapping Nanoantenna Arrays for Thin Film Solar Cells
We suggest a novel concept of efficient light-trapping structures for
thin-film solar cells based on arrays of planar nanoantennas operating far from
plasmonic resonances. The operation principle of our structures relies on the
excitation of chessboard-like collective modes of the nanoantenna arrays with
the field localized between the neighboring metal elements. We demonstrated
theoretically substantial enhancement of solar-cell short-circuit current by
the designed light-trapping structure in the whole spectrum range of the
solar-cell operation compared to conventional structures employing
anti-reflecting coating. Our approach provides a general background for a
design of different types of efficient broadband light-trapping structures for
thin-film solar-cell technologically compatible with large-area thin-film
fabrication techniques
Hall conductivity from dyonic black holes
A class of strongly interacting 2+1 dimensional conformal field theories in a
transverse magnetic field can be studied using the AdS/CFT duality. We compute
zero momentum hydrodynamic response functions of maximally supersymmetric 2+1
dimensional SU(N) Yang-Mills theory at the conformal fixed point, in the large
N limit. With background magnetic field B and electric charge density rho, the
Hall conductivity is found to be rho/B. The result, anticipated on kinematic
grounds in field theory, is obtained from perturbations of a four dimensional
AdS black hole with both electric and magnetic charges.Comment: 1+13 pages. TT correlator corrected. Typos corrected and added ref
A caloritronics-based Mott neuristor
Machine learning imitates the basic features of biological neural networks to
efficiently perform tasks such as pattern recognition. This has been mostly
achieved at a software level, and a strong effort is currently being made to
mimic neurons and synapses with hardware components, an approach known as
neuromorphic computing. CMOS-based circuits have been used for this purpose,
but they are non-scalable, limiting the device density and motivating the
search for neuromorphic materials. While recent advances in resistive switching
have provided a path to emulate synapses at the 10 nm scale, a scalable neuron
analogue is yet to be found. Here, we show how heat transfer can be utilized to
mimic neuron functionalities in Mott nanodevices. We use the Joule heating
created by current spikes to trigger the insulator-to-metal transition in a
biased VO2 nanogap. We show that thermal dynamics allow the implementation of
the basic neuron functionalities: activity, leaky integrate-and-fire,
volatility and rate coding. By using local temperature as the internal
variable, we avoid the need of external capacitors, which reduces neuristor
size by several orders of magnitude. This approach could enable neuromorphic
hardware to take full advantage of the rapid advances in memristive synapses,
allowing for much denser and complex neural networks. More generally, we show
that heat dissipation is not always an undesirable effect: it can perform
computing tasks if properly engineered
On the convergence of the gradient expansion in hydrodynamics
Hydrodynamic excitations corresponding to sound and shear modes in fluids are
characterised by gapless dispersion relations. In the hydrodynamic gradient
expansion, their frequencies are represented by power series in spatial
momenta. We investigate the analytic structure and convergence properties of
the hydrodynamic series by studying the associated spectral curve in the space
of complexified frequency and complexified spatial momentum. For the strongly
coupled supersymmetric Yang-Mills plasma, we use the holographic
duality methods to demonstrate that the derivative expansions have finite
non-zero radii of convergence. Obstruction to the convergence of hydrodynamic
series arises from level-crossings in the quasinormal spectrum at complex
momenta.Comment: V3: 5 pages, 2 figures. Final version. Published in Physical Review
Letters with the title "Convergence of the Gradient Expansion in
Hydrodynamics
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