A new X-ray diffraction study of the one-dimensional spin-Peierls compound α ′ -NaV2O5 reveals a centrosymmetric (Pmmn) crystal structure with one type of V site, contrary to the previously postulated non-centrosymmetric P21mn structure with two types of V sites (V +4 and V +5 ). Density functional calculations indicate that NaV2O5 is a quarter-filled ladder compound with the spins carried by V-O-V molecular orbitals on the rungs of the ladder. Estimates of the chargetransfer gap and the exchange coupling agree well with experiment and explain the insulating behavior of NaV2O5 and its magnetic properties. . A spin-Peierls system undergoes a lattice instability at T SP and for T < T SP the system dimerizes and a spin-gap opens. Here we propose that the spin-Peierls compound NaV 2 O 5 is at the same time a quarter-filled ladder system, in contrast to the previous notion which assumed NaV 2 O 5 to be made up of weakly coupled pairs of V +4 and V +5 chains [4,6]. Our proposition is based on a re-determination of the crystal structure of NaV 2 O 5 by X-ray diffraction and on density-functional calculations. Mapping of the density functional results on Hubbard and Heisenberg models yields values for the model parameters which explain readily the insulating behavior of NaV 2 O 5 and its the magnetic properties. Our results also show that NaV 2 O 5 and CaV 2 O 5 are isostructural and consequently establish CaV 2 O 5 as a half-filled ladder system.Crystal structure The crystal structure of α ′ -NaV 2 O 5 consists of double chains of edge-sharing distorted tetragonal VO 5 -pyramids running along the orthorhombic baxis, which are linked together via common corners of the pyramids to form sheets. These in turn are stacked

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Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender.The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution.Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and a an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance.We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for realworld phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts. The interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights.

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A technique to determine accurately transport properties of integrable and non-integrable quantum-spin chains at finite temperatures by Quantum Monte-Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of a Drude weight in the gapless regime of a non-integrable system with longer-ranged interactions is presented. We estimate the effect of the non-integrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.PACS numbers: 75.30.Gw, 75.10.Jm, 78.30.-j Introduction -During the last few years several families of materials containing well characterized quasi onedimensional spin-1/2 structures have been synthesized. The charge-transfer gap is in many cases large and the spin excitations contribute significantly to the thermal and magnetization transport at low temperatures. For example,63 Cu NMR studies 1 in Sr 2 CuO 3 have measured a spin diffusion coefficient (equivalent to diffusive magnetization transport) several orders of magnitude larger than the value for conventional diffusive systems, and thermal transport measurements in Sr 2 CuO 3 and SrCuO 2 indicate 2 quasi-ballistic transport with a mean-free path of several thousands ofÅ.These unusual results have been related to the peculiar physics of one-dimensional quantum chains. It is known that the spin transport in the XXZ chain

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