Criticality in correlated quantum matter

At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examining exact solutions of models of correlated systems and find that the temperature can be surprisingly high. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, $\rho_{s}(0)$, and the transition temperature, $T_{c}$, of the cuprates are related by $T_{c}\propto\rho_{s}(0)^y$, where the exponent $y$ is different at the two edges of the superconducting dome, signifying the respective QCPs. This relationship can be tested in high quality crystals.Comment: Final accepted version not including minor stylistic correction

The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result

We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space

Land Use Competition

This chapter introduces competition as a heuristic concept to analyse how specific land use practices establish themselves against possible alternatives. We briefly outline the global importance of land use practices as the material and symbolic basis for people’s livelihoods, particularly the provision of food security and well-being. We chart the development over time from research on land cover towards research on drivers of land use practices as part of an integrated land systems science. The increasingly spatially, temporally and functionally distributed nature of these drivers poses multiple challenges to research on land use practices. We propose the notion of ‘competition’ to respond to some of these challenges and to better understand how alternative land use practices are negotiated. We conceive of competition as a relational concept. Competition asks about agents in relation to each other, about the mode or the logic in which these relations are produced and about the material environments, practices and societal institutions through which they are mediated. While this has centrally to do with markets and prices, we deliberately open the concept to embrace more than economic perspectives. As such competition complements a broadening of analytical attention from the ‘who’, ‘what’ and ‘when’ to include prominently the ‘how’ and ‘why’ of particular land use practices and the question to whom this matters and ought to matter. We suggest that competition is an analytically productive concept, because it does not commit the analyst to a particular epistemological stance. It addresses reflexivity and feed-back, emergence and downward causation, history and response rates—concepts that all carry very different conceptual and analytical connotations in different disciplines. We propose to make these differences productive by putting them alongside each other through the notion of competition. Last not least, the heuristic lens of competition affords the combination of empirical and normative aspects, thus addressing land use practices in material, social and ethical terms

Designing social learning systems for integrating social sciences into policy processes: Some experiences of water managing.

Intuitively attractive, integration is widely held to be the key to more sustainable forms of natural resource managing. But while there have been many positive initiatives, researchers and policy-makers are under increasing pressure to integrate natural and social sciences with policy. This pressure arises because of the realization of the complexity of environmental situations characterized by uncertainties, interdependencies and multiple stakeholders. Faced with this complexity, new ways of thinking about and enabling social science and policy integration are required. The importance of framing in natural resource managing is discussed before the links between ideas of integration and systems thinking are explored. Social learning and design of social learning systems are introduced as a conceptual and methodological innovation to enable integration. Previous research on water managing is used to explore some practical issues and findings. The chapter concludes with a short commentary on the constraints and opportunities for designing social learning systems