Kondo decoherence: finding the right spin model for iron impurities in gold and silver

We exploit the decoherence of electrons due to magnetic impurities, studied via weak localization, to resolve a longstanding question concerning the classic Kondo systems of Fe impurities in the noble metals gold and silver: which Kondo-type model yields a realistic description of the relevant multiple bands, spin and orbital degrees of freedom? Previous studies suggest a fully screened spin $S$ Kondo model, but the value of $S$ remained ambiguous. We perform density functional theory calculations that suggest $S = 3/2$. We also compare previous and new measurements of both the resistivity and decoherence rate in quasi 1-dimensional wires to numerical renormalization group predictions for $S=1/2,1$ and 3/2, finding excellent agreement for $S=3/2$.Comment: 4 pages, 4 figures, shortened for PR

Dynamical laws of superenergy in General Relativity

The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an attempt to generalize to gravitation the energy-momentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which are remarkably similar to those of the energy-momentum tensor of electromagnetism. However, the physical role of these tensors in General Relativity has remained obscure and no interpretation has achieved wide acceptance. In principle, they cannot represent {\em energy} and the term {\em superenergy} has been coined for the hypothetical physical magnitude lying behind them. In this work we try to shed light on the true physical meaning of {\em superenergy} by following the same procedure which enables us to give an interpretation of the electromagnetic energy. This procedure consists in performing an orthogonal splitting of the Bel and Bel-Robinson tensors and analysing the different parts resulting from the splitting. In the electromagnetic case such splitting gives rise to the electromagnetic {\em energy density}, the Poynting vector and the electromagnetic stress tensor, each of them having a precise physical interpretation which is deduced from the {\em dynamical laws} of electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel and Bel-Robinson tensors is more complex but, as expected, similarities with electromagnetism are present. Also the covariant divergence of the Bel tensor is analogous to the covariant divergence of the electromagnetic energy-momentum tensor and the orthogonal splitting of the former is found. The ensuing {\em equations} are to the superenergy what the Poynting theorem is to electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more acknowledgments added. To appear in Classical and Quantum Gravit

Conformal Yano-Killing tensor for the Kerr metric and conserved quantities

Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel--Robinson tensor and is examined in Kerr spacetime. A new interpretation of the conserved quantity obtained is proposed.Comment: 29 page

Null cone preserving maps, causal tensors and algebraic Rainich theory

A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general properties in dimension N. We prove that rank-2 tensors which map the null cone on itself are causal. It is known that, to any tensor A on V there is a corresponding ``superenergy'' (s-e) tensor T{A} which always has the dominant property. We prove that, conversely, any symmetric rank-2 tensor with the dominant property can be written in a canonical way as a sum of N s-e tensors of simple forms. We show that the square of any rank-2 s-e tensor is proportional to the metric if N<5, and that this holds for the s-e tensor of any simple form for arbitrary N. Conversely, we prove that any symmetric rank-2 tensor T whose square is proportional to the metric must be, up to sign, the s-e of a simple p-form, and that the trace of T determines the rank p of the form. This generalises, both with respect to N and the rank p, the classical algebraic Rainich conditions, which are necessary and sufficient conditions for a metric to originate in some physical field, and has a geometric interpretation: the set of s-e tensors of simple forms is precisely the set of tensors which preserve the null cone and its time orientation. It also means that all involutory Lorentz transformations (LT) can be represented as s-e tensors of simple forms, and that any rank-2 s-e tensor is the sum of at most N conformally involutory LT. Non-symmetric null cone preserving maps are shown to have a causal symmetric part and are classified according to the null eigenvectors of the skew-symmetric part. We thus obtain a complete classification of all conformal LT and singular null cone preserving maps on V.Comment: 36 pages, no figures, LaTeX fil

Conservation laws for vacuum tetrad gravity

Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding symmetries with the same Lorentz algebra, and 10 corresponding conservation laws.Comment: Final version with additional reference

On the structure of the new electromagnetic conservation laws

New electromagnetic conservation laws have recently been proposed: in the absence of electromagnetic currents, the trace of the Chevreton superenergy tensor, $H_{ab}$ is divergence-free in four-dimensional (a) Einstein spacetimes for test fields, (b) Einstein-Maxwell spacetimes. Subsequently it has been pointed out, in analogy with flat spaces, that for Einstein spacetimes the trace of the Chevreton superenergy tensor $H_{ab}$ can be rearranged in the form of a generalised wave operator $\square_L$ acting on the energy momentum tensor $T_{ab}$ of the test fields, i.e., $H_{ab}=\square_LT_{ab}/2$. In this letter we show, for Einstein-Maxwell spacetimes in the full non-linear theory, that, although, the trace of the Chevreton superenergy tensor $H_{ab}$ can again be rearranged in the form of a generalised wave operator $\square_G$ acting on the electromagnetic energy momentum tensor, in this case the result is also crucially dependent on Einstein's equations; hence we argue that the divergence-free property of the tensor $H_{ab}=\square_GT_{ab}/2$ has significant independent content beyond that of the divergence-free property of $T_{ab}$

Magnetic spin excitations in Mn doped GaAs : A model study

We provide a quantitative theoretical model study of the dynamical magnetic properties of optimally annealed Ga$_{1-x}$Mn$_x$As. This model has already been shown to reproduce accurately the Curie temperatures for Ga$_{1-x}$Mn$_x$As. Here we show that the calculated spin stiffness are in excellent agreement with those which were obtained from ab-initio based studies. In addition, an overall good agreement is also found with available experimental data. We have also evaluated the magnon density of states and the typical density of states from which the "mobility edge", separating the extended from localized magnon states, was determined. The power of the model lies in its ability to be generalized for a broad class of diluted magnetic semiconductor materials, thus it bridges the gap between first principle calculations and model based studies.Comment: 5 pages, 5 figures, Text and some figures revised to match the accepted versio

Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples

Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causality in Lorentzian geometry. In the present paper, these tools are further developed in several directions such as: (i) causal mappings --and, thus, abstract chronological ones-- do not preserve two levels of the standard hierarchy of causality conditions (however, they preserve the remaining levels as shown in the above reference), (ii) even though global hyperbolicity is a stable property (in the set of all time-oriented Lorentzian metrics on a fixed manifold), the causal structure of a globally hyperbolic spacetime can be unstable against perturbations; in fact, we show that the causal structures of Minkowski and Einstein static spacetimes remain stable, whereas that of de Sitter becomes unstable, (iii) general criteria allow us to discriminate different causal structures in some general spacetimes (e.g. globally hyperbolic, stationary standard); in particular, there are infinitely many different globally hyperbolic causal structures (and thus, different conformal ones) on $\R^2$, (iv) plane waves with the same number of positive eigenvalues in the frequency matrix share the same causal structure and, thus, they have equal causal extensions and causal boundaries.Comment: 33 pages, 9 figures, final version (the paper title has been changed). To appear in Classical and Quantum Gravit

A Two-populations Ising model on diluted Random Graphs

We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the existence of a phase transition at a value of the inter-groups interaction coupling $J_{12}^C$ which depends algebraically on the dilution of the graph and on the relative width of the two populations, as explained by means of scaling arguments. We also measure the critical exponents, which are consistent with those of the Curie-Weiss model, hence suggesting a wide robustness of the universality class.Comment: 11 pages, 4 figure

Aneurysms—from traumatology to screening

This paper deals with aneurysmal disease, primarily when localized in the abdominal aorta. It is based on the Olof Rudbeck lecture 2009. Aneurysm is a localized widening of an artery, and its definition has become an important issue today when the disease is in focus for screening programmes. Aetiology and pathogenesis are still poorly understood, but a genetic component determining the strength of the aortic wall is important, and there is a strong male dominance. Historically, several attempts have been made to treat the disease, but reconstructive treatment has been possible only since 1951, in an increasing number of cases performed endovascularly. By early detection through screening, and thereby the possibility to treat before rupture, it has now become possible to decrease the total mortality from the disease in the population