Noether symmetry approach to scalar-field-dominated cosmology with dynamically evolving G and Lambda

This paper studies the cosmological equations for a scalar field Phi in the framework of a quantum gravity modified Einstein--Hilbert Lagrangian where G and Lambda are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Lambda = Lambda(G) and the potential V = V(Phi) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling.Comment: 10 pages, Revtex

Coupled structure-function responses to disturbance: High structural complexity resistance supports primary production resistance

The capacity of forests to resist structural change and retain material legacies–the biotic and abiotic resources that persist through disturbance–is crucial to sustaining ecosystem functioning after disturbance. However, the role of forest structure as both a material legacy and feature supporting carbon (C) cycling stability following disturbance has not been widely investigated. We used a large-scale disturbance manipulation to ask whether LiDAR-derived canopy structures as material legacies drive 3-year responses of NPP to a range of disturbance severity levels. As part of the Forest Resilience Threshold Experiment (FoRTE) in northern Michigan, USA we simulated phloem-disrupting disturbances at a range of severities and two disturbance types. We quantified the legacies of forest structure using two approaches: one measured change in structure and primary production from pre- to post-disturbance and the second estimated resistance as log transformed ratios of control and treatment values. We found that total aboveground wood net primary production (ANPPw) remained similar across disturbance severities as remnant trees rapidly increased rates of primary production. Experiment-wide, disturbance had limited effects on change in mean structural complexity values; however, high variance underscored large differences in the magnitude and direction of complexity’s response at the plot-scale. Plot-scale structural complexity, but not VAI, resistance strongly predicted ANPPw resistance while temporal VAI and structural complexity changes did not. We conclude that the presence of material legacies in the form of forest structure may affect primary production stability following disturbance, and that how legacies are quantified may affect the interpretation of disturbance response

Fractal properties of quantum spacetime

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of \k-Minkowski, the latter being relevant in the context of quantum gravity.Comment: 4 pages, 2 figures; some minor corrections; reference adde

Noncompact sigma-models: Large N expansion and thermodynamic limit

Noncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d \geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d=2 demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for ``criticality'' and ``triviality'' of the theories in the SO(1,N) invariant sector are discussed.Comment: 46 pages, 2 figure

The curious case of large-N expansions on a (pseudo)sphere

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.Comment: 18 pages, 3 figure