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 $SO(n+1)$-invariant Gaussian random polynomials on $\mathbb{RP}^n$ and systems of ${\rm isom}(\mathbb{R}^n)$-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 ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions we also obtain a fast decay of correlations at long distances. We then prove that the correlation function for the ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions is "universal," describing the scaling limit of the correlation function for the restriction of systems of the $SO(k+1)$-invariant Gaussian random polynomials to any $n$-dimensional $C^2$ submanifold $M \subset \mathbb{RP}^k$. 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 ${\cal N}=4$ 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