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

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

Non-perturbative embedding of local defects in crystalline materials

We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the difference Q between the density matrix of the defective crystal and the density matrix of the perfect crystal, in a basis of precomputed maximally localized Wannier functions of the reference perfect crystal. This approach can be used within any semi-empirical or Density Functional Theory framework.Comment: 13 pages, 4 figure

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

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

Phase transition close to room temperature in BiFeO3 thin films

BiFeO3 (BFO) multiferroic oxide has a complex phase diagram that can be mapped by appropriately substrate-induced strain in epitaxial films. By using Raman spectroscopy, we conclusively show that films of the so-called supertetragonal T-BFO phase, stabilized under compressive strain, displays a reversible temperature-induced phase transition at about 100\circ, thus close to room temperature.Comment: accepted in J. Phys.: Condens. Matter (Fast Track Communication

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

Have regional inequalities in life expectancy widened within the European Union between 1991 and 2008?

<b>BACKGROUND:</b> Health inequalities have widened within and between many European countries over recent decades, but Europe-wide sub-national trends have been largely overlooked. For regions across the European Union (EU), we assess how geographical inequalities (i.e., between regions) and sociospatial inequalities (i.e., between regions grouped by an area-level measure of average household income) in male and female life expectancy have changed between 1991 and 2008.<p></p> <b>METHODS:</b> Household income, life expectancy at birth and population count data were obtained for 129 regions (level 2 Nomenclature of Statistical Territorial Units, 'NUTS') in 13 European countries with 1991-2008 data (2008 population = 272 million). We assessed temporal changes in the range of life expectancies, for all regions and for Western and Eastern European regions separately.<p></p> <b>RESULTS:</b> Between 1991 and 2008, the geographical range of life expectancies found among European regions remained relatively constant, with the exception of life expectancy among male Eastern Europeans, for whom the range widened by 2.8 years. Sociospatial inequalities in life expectancy (1999-2008 data only) remained constant for all regions combined and for Western Europe, but more than doubled in size for male Eastern Europeans. For female Eastern Europeans, life expectancy was unrelated to regional household income.<p></p> <b>CONCLUSIONS:</b>Regional life-expectancy inequalities in the EU have not narrowed over 2 decades, despite efforts to reduce them. Household income differences across European regions may partly explain these inequalities. As inequalities transcend national borders, reduction efforts may require EU-wide coordination in addition to national efforts.<p></p&gt

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 $

Operationalising the 20-minute neighbourhood

BACKGROUND: Recent rapid growth in urban areas and the desire to create liveable neighbourhoods has brought about a renewed interest in planning for compact cities, with concepts like the 20-minute neighbourhood (20MN) becoming more popular. A 20MN broadly reflects a neighbourhood that allows residents to meet their daily (non-work) needs within a short, non-motorised, trip from home. The 20MN concept underpins the key planning strategy of Australia’s second largest city, Melbourne, however the 20MN definition has not been operationalised. This study aimed to develop and operationalise a practical definition of the 20MN and apply this to two Australian state capital cities: Melbourne (Victoria) and Adelaide (South Australia). METHODS: Using the metropolitan boundaries for Melbourne and Adelaide, data were sourced for several layers related to five domains: 1) healthy food; 2) recreational resources; 3) community resources; 4) public open space; and 5) public transport. The number of layers and the access measures required for each domain differed. For example, the recreational resources domain only required a sport and fitness centre (gym) within a 1.5-km network path distance, whereas the public open space domain required a public open space within a 400-m distance along a pedestrian network and 8 ha of public open space area within a 1-km radius. Locations that met the access requirements for each of the five domains were defined as 20MNs. RESULTS: In Melbourne 5.5% and in Adelaide 7.6% of the population were considered to reside in a 20MN. Within areas classified as residential, the median number of people per square kilometre with a 20MN in Melbourne was 6429 and the median number of dwellings per square kilometre was 3211. In Adelaide’s 20MNs, both population density (3062) and dwelling density (1440) were lower than in Melbourne. CONCLUSIONS: The challenge of operationalising a practical definition of the 20MN has been addressed by this study and applied to two Australian cities. The approach can be adapted to other contexts as a first step to assessing the presence of existing 20MNs and monitoring further implementation of this concept. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12966-021-01243-3