Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

A Modeling Analysis of Changing Global Land Use as affected by Changing Demands for Wood Products

The 21st century has brought new challenges for forest management at a time when globalization in world trade is increasing and global climate change is becoming increasingly apparent. In addition to various goods and services like food, feed, timber or biofuels being provided to humans, forest ecosystems are a large store of terrestrial carbon and account for a major part of the carbon exchange between the atmosphere and the land surface. Depending on the stage of the ecosystems and/or management regimes, forests can be either sinks, or sources of carbon. At the global scale, rapid economic development and a growing world population have raised much concern over the use of natural resources, especially forest resources. The challenging question is how can the global demands for forest commodities be satisfied in an increasingly globalised economy, and where could they potentially be produced? For this purpose, wood demand estimates need to be integrated in a framework, which is able to adequately handle the competition for land between major land-use options such as residential land or agricultural land. This thesis is organised in accordance with the requirements to integrate the simulation of forest changes based on wood extraction in an existing framework for global land-use modelling called LandSHIFT. Accordingly, the following neuralgic points for research have been identified: (1) a review of existing global-scale economic forest sector models (2) simulation of global wood production under selected scenarios (3) simulation of global vegetation carbon yields and (4) the implementation of a land-use allocation procedure to simulate the impact of wood extraction on forest land-cover. Modelling the spatial dynamics of forests on the global scale requires two important inputs: (1) simulated long-term wood demand data to determine future roundwood harvests in each country and (2) the changes in the spatial distribution of woody biomass stocks to determine how much of the resource is available to satisfy the simulated wood demands. First, three global timber market models are reviewed and compared in order to select a suitable economic model to generate wood demand scenario data for the forest sector in LandSHIFT. The comparison indicates that the ‘Global Forest Products Model’ (GFPM) is most suitable for obtaining projections on future roundwood harvests for further study with the LandSHIFT forest sector. Accordingly, the GFPM is adapted and applied to simulate wood demands for the global forestry sector conditional on selected scenarios from the Millennium Ecosystem Assessment and the Global Environmental Outlook until 2050. Secondly, the Lund-Potsdam-Jena (LPJ) dynamic global vegetation model is utilized to simulate the change in potential vegetation carbon stocks for the forested locations in LandSHIFT. The LPJ data is used in collaboration with spatially explicit forest inventory data on aboveground biomass to allocate the demands for raw forest products and identify locations of deforestation. Using the previous results as an input, a methodology to simulate the spatial dynamics of forests based on wood extraction is developed within the LandSHIFT framework. The land-use allocation procedure specified in the module translates the country level demands for forest products into woody biomass requirements for forest areas, and allocates these on a five arc minute grid. In a first version, the model assumes only actual conditions through the entire study period and does not explicitly address forest age structure. Although the module is in a very preliminary stage of development, it already captures the effects of important drivers of land-use change like cropland and urban expansion. As a first plausibility test, the module performance is tested under three forest management scenarios. The module succeeds in responding to changing inputs in an expected and consistent manner. The entire methodology is applied in an exemplary scenario analysis for India. A couple of future research priorities need to be addressed, particularly the incorporation of plantation establishments; issue of age structure dynamics; as well as the implementation of a new technology change factor in the GFPM which can allow the specification of substituting raw wood products (especially fuelwood) by other non-wood products.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Physiological analysis of central and peripheral insect circadian pacemaker neurons

Alle bisher untersuchten Lebewesen besitzen (circadiane) innere Uhren, die eine endogene Perioden-länge von ungefähr 24 Stunden generieren. Eine innere Uhr kann über Zeitgeber mit der Umwelt synchronisiert werden und ermöglicht dem Organismus, rhythmische Umweltveränderungen vorweg zu nehmen. Neben einem zentralen Schrittmacher, der Physiologie und Verhalten des Organismus steuert, gibt es in unterschiedlichen Organen auch periphere Uhren, die die zeitlichen Abläufe in der spezifischen Funktion dieser Organe steuern. In dieser Arbeit sollten zentrale und periphere Schrittmacherneurone von Insekten physiologisch untersucht und verglichen werden. Die Neurone der akzessorischen Medulla (AME) von Rhyparobia maderae dienten als Modellsystem für zentrale Schrittmacher, während olfaktorische Rezeptorneurone (ORNs) von Manduca sexta als Modellsystem für periphere Schrittmacher dienten. Die zentralen Schrittmacherneurone wurden in extrazellulären Ableitungen an der isolierten AME (Netzwerkebene) und in Patch-Clamp Experimenten an primären AME Zellkulturen (Einzelzellebene) untersucht. Auf Netzwerkebene zeigten sich zwei charakteristische Aktivitätsmuster: regelmäßige Aktivität und Wechsel zwischen hoher und niedriger Aktivität (Oszillationen). Es wurde gezeigt, dass Glutamat ein Neurotransmitter der weitverbreiteten inhibitorischen Synapsen der AME ist, und dass in geringem Maße auch exzitatorische Synapsen vorkommen. Das Neuropeptid pigment-dispersing factor (PDF), das von nur wenigen AME Neuronen exprimiert wird und ein wichtiger Kopplungsfaktor im circadianen System ist, führte zu Hemmungen, Aktivierungen oder Oszillationen. Die Effekte waren transient oder langanhaltend und wurden wahrscheinlich durch den sekundären Botenstoff cAMP vermittelt. Ein Zielmolekül von cAMP war vermutlich exchange protein directly activated by cAMP (EPAC). Auf Einzelzellebene wurde gezeigt, dass die meisten AME Neurone depolarisiert waren und deshalb nicht feuerten. Die Analyse von Strom-Spannungs-Kennlinien und pharmakologische Experimente ergaben, dass unterschiedliche Ionenkanäle vorhanden waren (Ca2+, Cl-, K+, Na+ Kanäle sowie nicht-spezifische Kationenkanäle). Starke, bei hohen Spannungen aktivierende Ca2+ Ströme (ICa) könnten eine wichtige Rolle bei Ca2+-abhängiger Neurotransmitter-Ausschüttung, Oszillationen, und Aktionspotentialen spielen. PDF hemmte unterschiedliche Ströme (ICa, IK und INa) und aktivierte nicht-spezifische Kationenströme (Ih). Es wurde angenommen, dass simultane PDF-abhängige Hyper- und Depolarisationen rhythmische Membranpotential-Oszillationen verursachen. Dieser Mechanismus könnte eine Rolle bei PDF-abhängigen Synchronisationen spielen. Die Analyse peripherer Schrittmacherneurone konzentrierte sich auf die Charakterisierung des olfaktorischen Corezeptors von M. sexta (MsexORCO). In anderen Insekten ist ORCO für die Membran-Insertion von olfaktorischen Rezeptoren (ORs) erforderlich. ORCO bildet Komplexe mit den ORs, die in heterologen Expressionssystemen als Ionenkanäle fungieren und Duft-Antworten vermitteln. Es wurde die Hypothese aufgestellt, dass MsexORCO in pheromonsensitiven ORNs in vivo nicht als Teil eines ionotropen Rezeptors sondern als Schrittmacherkanal fungiert, der unterschwellige Membranpotential-Oszillationen generiert. MsexORCO wurde mit vermeintlichen Pheromonrezeptoren in human embryonic kidney (HEK 293) Zellen coexprimiert. Immuncytochemie und Ca2+ Imaging Experimente zeigten sehr schwache Expressionsraten. Trotzdem war es möglich zu zeigen, dass MsexORCO wahrscheinlich ein spontan-aktiver, Ca2+-permeabler Ionenkanal ist, der durch den ORCO-Agonisten VUAA1 und cyclische Nucleotide aktiviert wird. Außerdem wiesen die Experimente darauf hin, dass MsexOR-1 offensichtlich der Bombykal-Rezeptor ist. Eine weitere Charakterisierung von MsexORCO in primären M. sexta ORN Zellkulturen konnte nicht vollendet werden, weil die ORNs nicht signifikant auf ORCO-Agonisten oder -Antagonisten reagierten.