Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields

Using the Pauli-Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac's vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi

Strain analysis of multiferroic BiFeO3-CoFe2O4 nanostructures by Raman scattering

We report a Raman scattering investigation of columnar BiFeO3-CoFe2O4 (BFO-CFO) epitaxial thin film nanostructures, where BFO pillars are embedded in a CFO matrix. The feasibility of a strain analysis is illustrated through an investigation of two nanostructures with different BFO-CFO ratios. We show that the CFO matrix presents the same strain state in both nanostructures, while the strain state of the BFO pillars depends on the BFO/CFO ratio with an increasing tensile strain along the out-of-plane direction with decreasing BFO content. Our results demonstrate that Raman scattering allows monitoring strain states in complex 3D multiferroic pillar/matrix composites.Comment: revised version submitted to Appl. Phys. Let

Self-consistent solution for the polarized vacuum in a no-photon QED model

We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted as the polarized vacuum and it solves a self-consistent equation. In a recent paper math-ph/0403005, we proved the convergence of the iterative fixed-point scheme naturally associated with this equation to a global minimizer of the BDF functional, under some restrictive conditions on the external potential, the ultraviolet cut-off $\Lambda$ and the bare fine structure constant $\alpha$. In the present work, we improve this result by showing the existence of the minimizer by a variational method, for any cut-off $\Lambda$ and without any constraint on the external field. We also study the behaviour of the minimizer as $\Lambda$ goes to infinity and show that the theory is "nullified" in that limit, as predicted first by Landau: the vacuum totally kills the external potential. Therefore the limit case of an infinite cut-off makes no sense both from a physical and mathematical point of view. Finally, we perform a charge and density renormalization scheme applying simultaneously to all orders of the fine structure constant $\alpha$, on a simplified model where the exchange term is neglected.Comment: Final version, to appear in J. Phys. A: Math. Ge

Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation

We consider a generalized Dirac-Fock type evolution equation deduced from no-photon Quantum Electrodynamics, which describes the self-consistent time-evolution of relativistic electrons, the observable ones as well as those filling up the Dirac sea. This equation has been originally introduced by Dirac in 1934 in a simplified form. Since we work in a Hartree-Fock type approximation, the elements describing the physical state of the electrons are infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced by Chaix-Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989), and recently established by Hainzl-Lewin-Sere, we prove the existence of global-in-time solutions of the considered evolution equation.Comment: 12 pages; more explanations added, some final (minor) corrections include

Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic x-ray scattering

The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and non-resonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom -- the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usual through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong, impacting ones ability to quantitively characterize the coupling. Here we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an 8-band model of copper oxides, we study the contributions from the lowest order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross-section as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and non-resonant x-ray scattering, as well as Raman and infrared conductivity.Comment: 10 pages, 10 figure

A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case

This article is concerned with the derivation and the mathematical study of a new mean-field model for the description of interacting electrons in crystals with local defects. We work with a reduced Hartree-Fock model, obtained from the usual Hartree-Fock model by neglecting the exchange term. First, we recall the definition of the self-consistent Fermi sea of the perfect crystal, which is obtained as a minimizer of some periodic problem, as was shown by Catto, Le Bris and Lions. We also prove some of its properties which were not mentioned before. Then, we define and study in details a nonlinear model for the electrons of the crystal in the presence of a defect. We use formal analogies between the Fermi sea of a perturbed crystal and the Dirac sea in Quantum Electrodynamics in the presence of an external electrostatic field. The latter was recently studied by Hainzl, Lewin, S\'er\'e and Solovej, based on ideas from Chaix and Iracane. This enables us to define the ground state of the self-consistent Fermi sea in the presence of a defect. We end the paper by proving that our model is in fact the thermodynamic limit of the so-called supercell model, widely used in numerical simulations.Comment: Final version, to appear in Comm. Math. Phy

Lattice and spin excitations in multiferroic h-YMnO3

We used Raman and terahertz spectroscopies to investigate lattice and magnetic excitations and their cross-coupling in the hexagonal YMnO3 multiferroic. Two phonon modes are strongly affected by the magnetic order. Magnon excitations have been identified thanks to comparison with neutron measurements and spin wave calculations but no electromagnon has been observed. In addition, we evidenced two additional Raman active peaks. We have compared this observation with the anti-crossing between magnon and acoustic phonon branches measured by neutron. These optical measurements underly the unusual strong spin-phonon coupling

Renormalization and asymptotic expansion of Dirac's polarized vacuum

We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant \alphaph, provided that the ultraviolet cut-off behaves as \Lambda\sim e^{3\pi(1-Z_3)/2\alphaph}\gg1. The renormalization parameter $

Confirmatory factor analysis of the French version of the Anticipatory and Consummatory Interpersonal Pleasure Scale

The Anticipatory and Consummatory Interpersonal Pleasure Scale (ACIPS), a measure specifically designed to assess hedonic capacity for social and interpersonal pleasure, was used to evaluate the presence of social anhedonia in patients as well as the general population. The first goal of this study was to validate the structure of the French version of the ACIPS. The second objective was to verify whether a one, two or three factor solution is most appropriate for the ACIPS scale. The French version of the ACIPS was tested on 263 French-speaking pre-graduate students or professional volunteers. For the confirmatory factor analysis, data were treated as categorical ordinal and all the models were estimated using a robust weighted least squares estimator with adjustments for the mean and variance. Three models were estimated. A one-factor model representing a general undifferentiated “pleasure” latent construct was first tested on the 17 ACIPS items. A two-factor model distinguishing anticipatory-pleasure and consummatory-pleasure was tested next. Finally, a three-factor model including intimate social interactions, group social interactions and social bonding was tested. The one and two-factor models showed a somewhat poor fit to the data. However, the goodness of fit of the three factor model was adequate. These results suggest that individuals who enjoyed interaction in one of these three sub domains were more likely to enjoy doing so in the two other domains. However, on the basis of the comparison between the one and three factor models, these three types interactions may not be considered as indistinguishable. Rather, they represent distinct and theoretically meaningful dimensions. These results show the French version of the ACIPS is a useful and valid scale to measure the capacity of savoring different kinds of social relationships

Magnetic properties of the honeycomb oxide Na2_2Co2_2TeO6_6

We have studied the magnetic properties of Na$_2$Co$_2$TeO$_6$, which features a honeycomb lattice of magnetic Co$^{2+}$ ions, through macroscopic characterization and neutron diffraction on a powder sample. We have shown that this material orders in a zig-zag antiferromagnetic structure. In addition to allowing a linear magnetoelectric coupling, this magnetic arrangement displays very peculiar spatial magnetic correlations, larger in the honeycomb planes than between the planes, which do not evolve with the temperature. We have investigated this behavior by Monte Carlo calculations using the $J_1$-$J_2$-$J_3$ model on a honeycomb lattice with a small interplane interaction. Our model reproduces the experimental neutron structure factor, although its absence of temperature evolution must be due to additional ingredients, such as chemical disorder or quantum fluctuations enhanced by the proximity to a phase boundary.Comment: 9 pages, 13 figure