Analytic continuation by averaging Pad\'e approximants

The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pad\'{e} approximants technique. We propose to remedy the well-known problems of the Pad\'{e} approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Pad\'{e} coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nano-ribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analysed in detail. The present approach is compared to a number of other techniques, i.e. the non-negative least-square method, the non-negative Tikhonov method and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions.Comment: 10 figure

Ecosystem properties and principles of living systems as foundation for sustainable agriculture – Critical reviews of environmental assessment tools, key findings and questions from a course process

With increasing demands on limited resources worldwide, there is a growing interest in sustainable patterns of utilisation and production. Ecological agriculture is a response to these concerns. To assess progress and compliance, standard and comprehensive measures of resource requirements, impacts and agro-ecological health are needed. Assessment tools should also be rapid, standardized, userfriendly, meaningful to public policy and applicable to management. Fully considering these requirements confounds the development of integrated methods. Currently, there are many methodologies for monitoring performance, each with its own foundations, assumptions, goals, and outcomes, dependent upon agency agenda or academic orientation. Clearly, a concept of sustainability must address biophysical, ecological, economic, and sociocultural foundations. Assessment indicators and criteria, however, are generally limited, lacking integration, and at times in conflict with one another. A result is that certification criteria, indicators, and assessment methods are not based on a consistent, underlying conceptual framework and often lack a management focus. Ecosystem properties and principles of living systems, including self-organisation, renewal, embeddedness, emergence and commensurate response provide foundation for sustainability assessments and may be appropriate focal points for critical thinking in an evaluation of current methods and standards. A systems framework may also help facilitate a comprehensive approach and promote a context for meaningful discourse. Without holistic accounts, sustainable progress remains an illdefined concept and an elusive goal. Our intent, in the work with this report, was to use systems ecology as a pedagogic basis for learning and discussion to: - Articulate general and common characteristics of living systems. - Identify principles, properties and patterns inherent in natural ecosystems. - Use these findings as foci in a dialogue about attributes of sustainability to: a. develop a model for communicating scientific rationale. b. critically evaluate environmental assessment tools for application in land-use. c. propose appropriate criteria for a comprehensive assessment and expanded definition of ecological land use

Microscopic origin of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe

By means of first principles calculations we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the $3d$ orbitals of $E_g$ and $T_{2g}$ symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly-interacting impurity levels. We demonstrate that, as a result of this, in Fe the $T_{2g}$ orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the $E_g$ states the Heisenberg picture breaks down, since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbour coupling indicates that the interactions among $E_g$ states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin.Comment: 5 pages, 4 figure

A theoretical analysis of the chemical bonding and electronic structure of graphene interacting with Group IA and Group VIIA elements

We propose a new class of materials, which can be viewed as graphene derivatives involving Group IA or Group VIIA elements, forming what we refer to as graphXene. We show that in several cases large band gaps can be found to open up, whereas in other cases a semimetallic behavior is found. Formation energies indicate that under ambient conditions, sp$^3$ and mixed sp$^2$/sp$^3$ systems will form. The results presented allow us to propose that by careful tuning of the relative concentration of the adsorbed atoms, it should be possible to tune the band gap of graphXene to take any value between 0 and 6.4 eV.Comment: 5 pages, 4 figures. Transferred to PR

Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups

In a previous paper we showed that the electromagnetic superenergy tensor, the Chevreton tensor, gives rise to a conserved current when there is a hypersurface orthogonal Killing vector present. In addition, the current is proportional to the Killing vector. The aim of this paper is to extend this result to the case when we have a two-parameter Abelian isometry group that acts orthogonally transitive on non-null surfaces. It is shown that for four-dimensional Einstein-Maxwell theory with a source-free electromagnetic field, the corresponding superenergy currents lie in the orbits of the group and are conserved. A similar result is also shown to hold for the trace of the Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon theory for the superenergy of the scalar field. This links up well with the fact that the Bel tensor has these properties and the possibility of constructing conserved mixed currents between the gravitational field and the matter fields.Comment: 15 page