Four Dimensional Graphene

Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond lattice H_4. We first study the link between the H_4 and SU(5); then we refine the BBTW 4D lattice action by using the weight vectors \lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5 of the 5-dimensional representation of SU(5) satisfying {\Sigma}_i\lambda_i=0. After that we study explicitly the solutions of the zeros of the Dirac operator D in terms of the SU(5) simple roots \alpha_1, \alpha_2, \alpha_3, \alpha_4 generating H_4; and its fundamental weights \omega_1, \omega_2, \omega_3, \omega_4 which generate the reciprocal lattice H_4^\ast. It is shown, amongst others, that these zeros live at the sites of H_4^\ast; and the continuous limit D is given by ((id\surd5)/2) \gamma^\muk_\mu with d, \gamma^\mu and k_\mu standing respectively for the lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector. Other features such as differences with BBTW model as well as the link between the Dirac operator following from our construction and the one suggested by Creutz using quaternions, are also given. Keywords: Graphene, Lattice QCD, 4D hyperdiamond, BBTW model, SU(5) Symmetry.Comment: LaTex, 26 pages, 1 figure, To appear in Phys Rev

Extremal Black Attractors in 8D Maximal Supergravity

Motivated by the new higher D-supergravity solutions on intersecting attractors obtained by Ferrara et al. in [Phys.Rev.D79:065031-2009], we focus in this paper on 8D maximal supergravity with moduli space [SL(3,R)/SO(3)]x[SL(2,R)/SO(2)] and study explicitly the attractor mechanism for various configurations of extremal black p- branes (anti-branes) with the typical near horizon geometries AdS_{p+2}xS^{m}xT^{6-p-m} and p=0,1,2,3,4; 2<=m<=6. Interpretations in terms of wrapped M2 and M5 branes of the 11D M-theory on 3-torus are also given. Keywords: 8D supergravity, black p-branes, attractor mechanism, M-theory.Comment: 37 page

Second-order optimisation strategies for neural network quantum states

The Variational Monte Carlo method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ans\"atze have been designed to tackle a wide variety of quantum many-body problems, modest progress has been made on the associated optimisation algorithms. In this work, we revisit the Kronecker Factored Approximate Curvature, an optimiser that has been used extensively in a variety of simulations. We suggest improvements on the scaling and the direction of this optimiser, and find that they substantially increase its performance at a negligible additional cost. We also reformulate the Variational Monte Carlo approach in a game theory framework, to propose a novel optimiser based on decision geometry. We find that, on a practical test case for continuous systems, this new optimiser consistently outperforms any of the KFAC improvements in terms of stability, accuracy and speed of convergence. Beyond Variational Monte Carlo, the versatility of this approach suggests that decision geometry could provide a solid foundation for accelerating a broad class of machine learning algorithms.Comment: 32 pages, 9 figures, 4 tables. Submitted to PRS

Reduction of Conducted Perturbations in DC-DC Voltage Converters by a Dual Randomized PWM Scheme

Randomized Pulse Width Modulation (RPWM) deals better than Deterministic PWM (DPWM) with Electro-Magnetic Compatibility (EMC) standards for conducted Electro-Magnetic Interferences (EMI). In this paper, we propose a dual RPWM scheme for DC-DC voltage converters: the buck converter and the full bridge converter. This scheme is based on the comparison of deterministic reference signals (one signal for the buck converter and two signals for the full bridge converter) to a single triangular carrier having two randomized parameters. By using directly the randomized parameters of the carrier, a mathematical model of the Power Spectral Density (PSD) of output voltage is developed for each converter. The EMC advantage of the proposed dual randomization scheme compared to the classical simple randomization schemes is clearly highlighted by the PSD analysis and confirmed by FFT (Fast Fourier Transform) analysis of the output voltage

Transient Analysis of Grounding Systems Associated to Substation Structures under Lightning Strokes

In this paper we propose a new formalism for analyzing the transient behavior of grounding systems associated to substation structures (Faraday-cage) under lightning strokes in unsettled regime. The protective device to study is formed of a guard filet connected to a grounding grid by simple conductors called down conductors. Our formalism is based on the resolution of the propagation equation in potential on 3D. The purpose of our proposition is the direct analyzing in time domain and simple implementation. We compare the results obtained by this new approach to results published in literature

Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states

We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the wavefunction and use machine learning techniques to variationally minimize the energy of systems from 2 to 6 particles. We provide extensive benchmarks with other many-body methods, including exact diagonalisation and the Hartree-Fock approximation. The neural quantum state provides the best energies across a wide range of interaction strengths. We find very different ground states depending on the sign of the interaction. In the non-perturbative repulsive regime, the system asymptotically reaches crystalline order. In contrast, the strongly attractive regime shows signs of bosonization. The neural quantum state continuously learns these different phases with an almost constant number of parameters and a very modest increase in computational time with the number of particles