Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

Reply to Comment on "Cosmic rays, carbon dioxide, and climate"

In our analysis [Rahmstorf et al., 2004], we arrived at two main conclusions: the data of Shaviv and Veizer [2003] do not show a significant correlation of cosmic ray flux (CRF) and climate, and the authors' estimate of climate sensitivity to CO2 based on a simple regression analysis is questionable. After careful consideration of Shaviv and Veizer's comment, we want to uphold and reaffirm these conclusions. Concerning the question of correlation, we pointed out that a correlation arose only after several adjustments to the data, including shifting one of the four CRF peaks and stretching the time scale. To calculate statistical significance, we first need to compute the number of independent data points in the CRF and temperature curves being correlated, accounting for their autocorrelation. A standard estimate [Quenouille, 1952] of the number of effective data points is urn:x-wiley:00963941:media:eost14930:eost14930-math-0001 where N is the total number of data points and r1, r2 are the autocorrelations of the two series. For the curves of Shaviv and Veizer [2003], the result is NEFF = 4.8. This is consistent with the fact that these are smooth curves with four humps, and with the fact that for CRF the position of the four peaks is determined by four spiral arm crossings or four meteorite clusters, respectively; that is, by four independent data points. The number of points that enter the calculation of statistical significance of a linear correlation is (NEFF− 2), since any curves based on only two points show perfect correlation; at least three independent points are needed for a meaningful result

Symmetry and disorder of the vitreous vortex lattice in an overdoped BaFe_{2-x}Co_xAs_2 superconductor: Indication for strong single-vortex pinning

The disordered flux line lattice in single crystals of the slightly overdoped aFe_{2-x}Co_xAs_2 (x = 0.19, Tc = 23 K) superconductor is studied by magnetization measurements, small-angle neutron scattering (SANS), and magnetic force microscopy (MFM). In the whole range of magnetic fields up to 9 T, vortex pinning precludes the formation of an ordered Abrikosov lattice. Instead, a vitreous vortex phase (vortex glass) with a short-range hexagonal order is observed. Statistical processing of MFM datasets lets us directly measure its radial and angular distribution functions and extract the radial correlation length \zeta. In contrast to predictions of the collective pinning model, no increase in the correlated volume with the applied field is observed. Instead, we find that \zeta decreases as 1.3*R1 ~ H^(-1/2) over four decades of the applied magnetic field, where R1 is the radius of the first coordination shell of the vortex lattice. Such universal scaling of \zeta implies that the vortex pinning in iron arsenides remains strong even in the absence of static magnetism. This result is consistent with all the real- and reciprocal-space vortex-lattice measurements in overdoped as-grown aFe_{2-x}Co_xAs_2 published to date and is thus sample-independent. The failure of the collective pinning model suggests that the vortices remain in the single-vortex pinning limit even in high magnetic fields up to 9 T.Comment: 11 pages, 6 figure

Symmetry and disorder of the vitreous vortex lattice in an overdoped BaFe_{2-x}Co_xAs_2 superconductor: Indication for strong single-vortex pinning

The disordered flux line lattice in single crystals of the slightly overdoped aFe_{2-x}Co_xAs_2 (x = 0.19, Tc = 23 K) superconductor is studied by magnetization measurements, small-angle neutron scattering (SANS), and magnetic force microscopy (MFM). In the whole range of magnetic fields up to 9 T, vortex pinning precludes the formation of an ordered Abrikosov lattice. Instead, a vitreous vortex phase (vortex glass) with a short-range hexagonal order is observed. Statistical processing of MFM datasets lets us directly measure its radial and angular distribution functions and extract the radial correlation length \zeta. In contrast to predictions of the collective pinning model, no increase in the correlated volume with the applied field is observed. Instead, we find that \zeta decreases as 1.3*R1 ~ H^(-1/2) over four decades of the applied magnetic field, where R1 is the radius of the first coordination shell of the vortex lattice. Such universal scaling of \zeta implies that the vortex pinning in iron arsenides remains strong even in the absence of static magnetism. This result is consistent with all the real- and reciprocal-space vortex-lattice measurements in overdoped as-grown aFe_{2-x}Co_xAs_2 published to date and is thus sample-independent. The failure of the collective pinning model suggests that the vortices remain in the single-vortex pinning limit even in high magnetic fields up to 9 T.Comment: 11 pages, 6 figure

Microstructure, mechanical behaviour and fracture of pure tungsten wire after different heat treatments

Plastic deformation of tungsten wire is an effective source of toughening tungsten fibre-reinforced tungsten composites (Wf/W) and other tungsten fibre-reinforced composites. To provide a reference for optimization of those composites, unconstrained pure tungsten wire is studied after various heat treatments in terms of microstructure, mechanical behaviour and fracture mode. Recrystallization is already observed at a relatively low temperature of 1273 K due to the large driving force caused by a high dislocation density. Annealing for 30 min at 1900 K also leads to recrystallization, but causes a rather different microstructure. As-fabricated wire and wire recrystallized at 1273 K for 3 h show fine grains with a high aspect ratio and a substantial plastic deformability: a clearly defined tensile strength, high plastic work, similar necking shape, and the characteristic knife-edge-necking of individual grains on the fracture surface. While the wire recrystallized at 1900 K displays large, almost equiaxed grains with low aspect ratios as well as distinct brittle properties. Therefore, it is suggested that a high aspect ratio of the grains is important for the ductile behaviour of tungsten wire and that embrittlement is caused by the loss of the preferable elongated grain structure rather than by recrystallization. In addition, a detailed evaluation of the plastic deformation behaviour during tensile test gives guidance to the design and optimization of tungsten fibre-reinforced composites

A skipping rope translocation mechanism in a widespread family of DNA repair helicases

Mitomycin repair factor A represents a family of DNA helicases that harbor a domain of unknown function DUF1998 and support repair of mitomycin Cinduced DNA damage by presently unknown molecular mechanisms. We determined crystal structures of Bacillus subtilis Mitomycin repair factor A alone and in complex with an ATP analog and or DNA and conducted structure informed functional analyses. Our results reveal a unique set of auxiliary domains appended to a dual RecA domain core. Upon DNA binding, a Zn2 binding domain, encompassing the domain of unknown function, acts like a drum that rolls out a canopy of helicase associated domains, entrapping the substrate and tautening an inter domain linker across the loading strand. Quantification of DNA binding, stimulated ATPase and helicase activities in the wild type and mutant enzyme variants in conjunction with themode of coordination of the ATP analog suggest that Mitomycin repair factor A employs similar ATPase driven conformational changes to translocate on DNA, with the linker ratcheting through the nucleotides like a skipping rope . The electrostatic surface topology outlines a likely path for the displaced DNA strand. Our results reveal unique molecular mechanisms in a widespread family of DNA repair helicases linked to bacterial antibiotics resistanc

Cumulant Expansions and the Spin-Boson Problem

The dynamics of the dissipative two-level system at zero temperature is studied using three different cumulant expansion techniques. The relative merits and drawbacks of each technique are discussed. It is found that a new technique, the non-crossing cumulant expansion, appears to embody the virtues of the more standard cumulant methods.Comment: 26 pages, LaTe