A differential identity for Green functions

If P is a differential operator with constant coefficients, an identity is derived to calculate the action of exp(P) on the product of two functions. In many-body theory, P describes the interaction Hamiltonian and the identity yields a hierarchy of Green functions. The identity is first derived for scalar fields and the standard hierarchy is recovered. Then the case of fermions is considered and the identity is used to calculate the generating function for the Green functions of an electron system in a time-dependent external potential.Comment: 14 page

Towards an evolutionary approach to sustainability transitions in tourism

Postprin

Site symmetry and crystal symmetry: a spherical tensor analysis

The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet.Comment: 27 pages, 3 figure

Relativistic corrections in magnetic systems

We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green's function in terms of the non-relativistic Green's function is first derived and then used to calculate the effective Hamiltonian, i.e., Pauli Hamiltonian, and effective velocity operator in the weak-relativistic limit. We point out that, besides neglecting orbital magnetism effects, the approximate Kohn-Sham-Dirac equation also gives relativistic corrections which differ from those of the exact Kohn-Sham-Dirac equation. These differences have quite serious consequences: in particular, the magnetocrystalline anisotropy of an uniaxial ferromagnet and the anisotropic magnetoresistance of a cubic ferromagnet are found from the approximate Kohn-Sham-Dirac equation to be of order $1/c^2$, whereas the correct results obtained from the exact Kohn-Sham-Dirac equation are of order $1/c^4$ . We give a qualitative estimate of the order of magnitude of these spurious terms

K-edge X-ray absorption spectra in transition metal oxides beyond the single particle approximation: shake-up many body effects

The near edge structure (XANES) in K-edge X-ray absorption spectroscopy (XAS) is a widely used tool for studying electronic and local structure in materials. The precise interpretation of these spectra with the help of calculations is hence of prime importance, especially for the study of correlated materials which have a complicated electronic structure per se. The single particle approach, for example, has generally limited itself to the dominant dipolar cross-section. It has long been known however that effects beyond this approach should be taken into account, both due to the inadequacy of such calculations when compared to experiment and the presence of shake-up many-body satellites in core-level photoemission spectra of correlated materials. This effect should manifest itself in XANES spectra and the question is firstly how to account for it theoretically and secondly how to verify it experimentally. By using state-of-the-art first principles electronic structure calculations and 1s photoemission measurements we demonstrate that shake-up many-body effects are present in K-edge XAS dipolar spectra of NiO, CoO and CuO at all energy scales. We show that shake-up effects can be included in K-edge XAS spectra in a simple way by convoluting the single-particle first-principles calculations including core-hole effects with the 1s photoemission spectra. We thus describe all features appearing in the XAS dipolar cross-section of NiO and CoO and obtain a dramatic improvement with respect to the single-particle calculation in CuO. These materials being prototype correlated magnetic oxides, our work points to the presence of shake-up effects in K-edge XANES of most correlated transition metal compounds and shows how to account for them, paving the way to a precise understanding of their electronic structure.Comment: 6 pages, 4 picture

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Rare earth contributions to the X-ray magnetic circular dichroism at the Co K edge in rare earth-cobalt compounds investigated by multiple-scattering calculations

The X-ray magnetic circular dichroism (XMCD) has been measured at the Co K edge in Co-hcp and R-Co compounds (R=La, Tb, Dy). The structure of the experimental XMCD spectra in the near-edge region has been observed to be highly sensitive to the magnetic environment of the absorbing site. Calculations of the XMCD have been carried out at the Co K edge in Co metal, LaCo$_5$ and TbCo$_5$ within the multiple-scattering framework including the spin-orbit coupling. In the three systems, the XMCD spectra in the near-edge region are well reproduced. The possibility to separate and quantitatively estimate the local effects from those due to the neighboring atoms in the XMCD cross section makes possible a more physical understanding of the spectra. The present results emphasize the major role played by the $d$ states of the Tb ions in the XMCD spectrum at the Co K edge in the TbCo$_5$ compound.Comment: 34 pages, revtex, 10 eps figures included with epsf, after referee revie

The structure of Green functions in quantum field theory with a general state

In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.Comment: 13 pages, 6 figure

Quantum field theory and Hopf algebra cohomology

We exhibit a Hopf superalgebra structure of the algebra of field operators of quantum field theory (QFT) with the normal product. Based on this we construct the operator product and the time-ordered product as a twist deformation in the sense of Drinfeld. Our approach yields formulas for (perturbative) products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods. Employing Hopf algebra cohomology sheds new light on the structure of QFT and allows the extension to interacting (not necessarily perturbative) QFT. We give a reconstruction theorem for time-ordered products in the spirit of Streater and Wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle. We also demonstrate how non-trivial vacua are described in our approach solving a problem in quantum chemistry.Comment: 39 pages, no figures, LaTeX + AMS macros; title changed, minor corrections, references update

X-ray Linear Dichroism in cubic compounds: the case of Cr3+ in MgAl2O4

The angular dependence (x-ray linear dichroism) of the Cr K pre-edge in MgAl2O4:Cr3+ spinel is measured by means of x-ray absorption near edge structure spectroscopy (XANES) and compared to calculations based on density functional theory (DFT) and ligand field multiplet theory (LFM). We also present an efficient method, based on symmetry considerations, to compute the dichroism of the cubic crystal starting from the dichroism of a single substitutional site. DFT shows that the electric dipole transitions do not contribute to the features visible in the pre-edge and provides a clear vision of the assignment of the 1s-->3d transitions. However, DFT is unable to reproduce quantitatively the angular dependence of the pre-edge, which is, on the other side, well reproduced by LFM calculations. The most relevant factors determining the dichroism of Cr K pre-edge are identified as the site distortion and 3d-3d electronic repulsion. From this combined DFT, LFM approach is concluded that when the pre-edge features are more intense than 4 % of the edge jump, pure quadrupole transitions cannot explain alone the origin of the pre-edge. Finally, the shape of the dichroic signal is more sensitive than the isotropic spectrum to the trigonal distortion of the substitutional site. This suggests the possibility to obtain quantitative information on site distortion from the x-ray linear dichroism by performing angular dependent measurements on single crystals