Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Soil biogenic emissions of nitric oxide from arid and semi-arid ecosystems

The biogenic production of NO in the soil accounts for between 10% and 40% of the global total. A large degree of the uncertainty in the estimation of the biogenic emissions stems from a shortage of measurements in arid regions, which comprise 40% of the earth’s land surface area. This study examined the emission of NO from three ecosystems in southern Africa which cover an aridity gradient from semi-arid savannas in South Africa to the hyper-arid Namib Desert in Namibia. A laboratory method was used to determine the release of NO as a function of the soil moisture and the soil temperature. Various methods were used to up-scale the net potential NO emissions determined in the laboratory to the vegetation patch, landscape or regional level. The importance of landscape, vegetation and climatic characteristics is emphasized. The first study occurred in a semi-arid savanna region in South Africa, where soils were sampled from 4 landscape positions in the Kruger National Park. The maximum NO emission occurred at soil moisture contents of 10%-20% water filled pore space (WFPS). The highest net potential NO emissions came from the low lying landscape positions, which have the largest nitrogen (N) stocks and the largest input of N. Net potential NO fluxes obtained in the laboratory were converted in field fluxes for the period 2003-2005, for the four landscape positions, using soil moisture and temperature data obtained in situ at the Kruger National Park Flux Tower Site. The NO emissions ranged from 1.5-8.5 kg ha-1 a-1. The field fluxes were up-scaled to a regional basis using geographic information system (GIS) based techniques, this indicated that the highest NO emissions occurred from the Midslope positions due to their large geographical extent in the research area. Total emissions ranged from 20x103 kg in 2004 to 34x103 kg in 2003 for the 56000 ha Skukuza land type. The second study occurred in an arid savanna ecosystem in the Kalahari, Botswana. In this study I collected soils from four differing vegetation patch types including: Pan, Annual Grassland, Perennial Grassland and Bush Encroached patches. The maximum net potential NO fluxes ranged from 0.27 ng m-2 s-1 in the Pan patches to 2.95 ng m-2 s-1 in the Perennial Grassland patches. The net potential NO emissions were up-scaled for the year December 2005-November 2006. This was done using 1) the net potential NO emissions determined in the laboratory, 2) the vegetation patch distribution obtained from LANDSAT NDVI measurements 3) estimated soil moisture contents obtained from ENVISAT ASAR measurements and 4) soil surface temperature measurements using MODIS 8 day land surface temperature measurements. This up-scaling procedure gave NO fluxes which ranged from 1.8 g ha-1 month-1 in the winter months (June and July) to 323 g ha-1 month-1 in the summer months (January-March). Differences occurred between the vegetation patches where the highest NO fluxes occurred in the Perennial Grassland patches and the lowest in the Pan patches. Over the course of the year the mean up-scaled NO emission for the studied region was 0.54 kg ha-1 a-1 and accounts for a loss of approximately 7.4% of the estimated N input to the region. The third study occurred in the hyper-arid Namib Desert in Namibia. Soils were sampled from three ecosystems; Dunes, Gravel Plains and the Riparian zone of the Kuiseb River. The net potential NO flux measured in the laboratory was used to estimate the NO flux for the Namib Desert for 2006 using modelled soil moisture and temperature data from the European Centre for Medium Range Weather Forecasts (ECMWF) operational model on a 36km x 35km spatial resolution. The maximum net potential NO production occurred at low soil moisture contents (<10%WFPS) and the optimal temperature was 25°C in the Dune and Riparian ecosystems and 35°C in the Gravel Plain Ecosystems. The maximum net potential NO fluxes ranged from 3.0 ng m-2 s-1 in the Riparian ecosystem to 6.2 ng m-2 s-1 in the Gravel Plains ecosystem. Up-scaling the net potential NO flux gave NO fluxes of up to 0.062 kg ha-1 a-1 in the Dune ecosystem and 0.544 kg h-1 a-1 in the Gravel Plain ecosystem. From these studies it is shown that NO is emitted ubiquitously from terrestrial ecosystems, as such the NO emission potential from deserts and scrublands should be taken into account in the global NO models. The emission of NO is influenced by various factors such as landscape, vegetation and climate. This study looks at the potential emissions from certain arid and semi-arid environments in southern Africa and other parts of the world and discusses some of the important factors controlling the emission of NO from the soil.

Response of nutrient cycles of an old-growth montane forest in Ecuador to experimental low-level nutrient amendments

Atmospheric nitrogen (N) and phosphorus (P) depositions are expected to increase in the tropicsrnas a consequence of increasing human activities in the next decades. Furthermore, a possiblernshortened El Niño Southern Oscillation cycle might come along with more frequent calcium (Ca)rndepositions on the eastern slope of the Ecuadorian Andes originating from Saharan dust. It isrncrucial to understand the response of the old-growth montane forest in Ecuador to increasedrnnutrient deposition to predict the further development of this megadiverse ecosystem.rnI studied experimental additions of N, P, N+P and Ca to the forest and an untreatedrncontrol, all in a fourfold replicated randomized block design. These experiments were conductedrnin the framework of a collaborative research effort, the NUtrient Manipulation EXperimentrn(NUMEX). I collected litter leachate, mineral soil solution (0.15 and 0.30 m depths), throughfallrnand fine litterfall samples and determined N, P and Ca concentrations and fluxes. This approachrnalso allowed me to assess whether N, P and/or Ca are limiting nutrients for forest growth.rnFurthermore, I evaluated the response of fine root biomass, leaf area index, leaf area and specificrnleaf area, tree diameter growth and basal area increment contributed from a cooperating group inrnthe Ca applied and control treatments.rnDuring the observation period of 16 months after the first fertilizer application, less thanrn10, 1 and 5% of the applied N, P and Ca, respectively, leached below the organic layer whichrncontained almost all roots but no significant leaching losses occurred to the deeper mineral soil.rnDeposited N, P and Ca from the atmosphere in dry and wet form were, on balance, retained in therncanopy in the control treatment. Retention of N, P and Ca in the canopy in their respectiverntreatments was reduced resulting in higher concentrations and fluxes of N, P and Ca inrnthroughfall and litterfall. Up to 2.5% of the applied N and 2% of the applied P and Ca werernrecycled to the soil with throughfall. Fluxes of N, P and Ca in throughfall+litterfall were higher inrnthe fertilized treatments than in the control; up to 20, 5 and 25% of the applied N, P and Ca,rnrespectively, were recycled to the soil with throughfall+litterfall.rnIn the Ca-applied plots, fine root biomass decreased significantly. Also the leaf area of thernfour most common tree species tended to decrease and the specific leaf area increasedrnsignificantly in Graffenrieda emarginata Triana, the most common tree species in the study area.rnThese changes are known plant responses to reduced nutrient stress. Reduced aluminium (Al)rntoxicity as an explanation of the Ca effect was unlikely, because of almost complete organocomplexationrnof Al and molar Ca:Al concentration ratios in solution above the toxicity threshold.rnThe results suggest that N, P and Ca co-limit the forest ecosystem functioning in thernnorthern Andean montane forests in line with recent assumptions in which different ecosystemrncompartments and even different phenological stages may show different nutrient limitationsrn(Kaspari et al. 2008). I conclude that (1) the expected elevated N and P deposition will bernretained in the ecosystem, at least in the short term and hence, quality of river water will not bernendangered and (2) increased Ca input will reduce nutrient stress of the forest.