Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

On the renormalization flow representation of field theory and some applications

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.

Sensitivity enhancement in NMR by using parahydrogen induced polarization

Enhancing the sensitivity of nuclear magnetic resonance measurements via hyperpolarization techniques like parahydrogen induced polarization (PHIP) is of high interest for spectroscopic investigations. Parahydrogen induced polarization is a chemical method, which makes use of the correlation between nuclear spins in parahydrogen to create hyperpolarized molecules. The key feature of this technique is the pairwise and simultaneous transfer of the two hydrogen atoms of parahydrogen to a double or triple bond resulting in a population of the Zeeman energy levels different from the Boltzmann equation. The obtained hyperpolarization results in antiphase peaks in the NMR spectrum with high intensities. Due to these strong NMR signals, this method finds arnlot of applications in chemistry e.g. the characterization of short-lived reaction intermediates. Also in medicine it opens up the possibility to boost the sensitivity of medical diagnostics via magnetic labeling of active contrast agents. Thus, further examination and optimization of the PHIP technique is of significant importance in order to achieve the highest possible sensitivity gain.rnrnIn this work, different aspects concerning PHIP were studied with respect to its chemical and spectroscopic background. The first part of this work mainly focused on optimizing the PHIP technique by investigating different catalyst systems and developing new setups for the parahydrogenation. Further examinations facilitated the transfer of the generated polarization from the protons to heteronuclei like 13C. The second part of this thesis examined the possibility to transfer these results to different biologically active compounds to enable their later application in medical diagnostics. Onerngroup of interesting substances is represented by metabolites or neurotransmitters in mammalian cells. Other interesting substances are clinically relevant drugs like a barbituric acid derivative or antidepressant drugs like citalopram which were investigated with regard to their applicability for the PHIP technique and the possibility to achievernpolarization transfer to 13C nuclei. The last investigated substrate is a polymerizable monomer whose polymer was used as a blood plasma expander for trauma victims after the first half of the 20th century. In this case, the utility of the monomer for the PHIP technique as a basis for later investigations of a polymerization reaction using hyperpolarized monomers was examined.rnrnHence, this thesis covers the optimization of the PHIP technology, hereby combining different fields of research like chemical and spectroscopical aspects, and transfers the results to applications of real biologally acitve compounds.

Spurenanalyse von Aktiniden in der Umwelt mittels Resonanzionisations-Massenspektrometrie

In dieser Arbeit wurde die Methode der resonanten Ionisation von neutralen Atomen mittels Laserstrahlung auf die leichten Aktinide Thorium, Uran, Neptunium und Plutonium angewendet und für die Ultraspurenanalyse optimiert. Der empfindliche Nachweis dieser Aktinide stellt eine Herausforderung für die Beobachtung und Bestimmung von radioaktiven Verunreinigungen aus kerntechnischen Anlagen in der Umwelt dar. In einem für diese Untersuchungen entwickelten Quadrupolmassenspektrometer konnte durch Resonanzionisationsspektroskopie jeweils eine Reihe unbekannter Energiezustände in der Elektronenhülle des neutralen Atoms der oben genannten Aktinide identifiziert, sowie effiziente Anregungsschemata für die resonante Ionisation entwickelt und charakterisiert werden. Durch die verwendete in-source-Ionisation, die aufgrund der guten Überlagerung von Laserstrahlung und Atomstrahl eine hohe Nachweiseffizienz gewährleistet, konnten diese Untersuchungen bereits mit einem, für Radionuklide notwendigen, geringen Probeneintrag erfolgen. Die resonante Ionisation erlaubt durch die selektiven resonanten Prozesse eine Unterdrückung unerwünschter Kontaminationen und wurde auf den analytischen Nachweis von Ultraspurengehalten in Umweltproben, sowie die Bestimmung der entsprechenden Isotopenzusammensetzung optimiert. Durch die effiziente in-source-Ionisation mit leistungsstarker gepulster Laserstrahlung, konnten Nachweiseffizienzen im Bereich von bis zu 1% erreicht werden. Dabei wurden für Plutonium in synthetischen Proben, aber auch in ersten Umweltproben, Nachweisgrenzen von 10^4-10^5 Atomen erzielt. Die Verwendung spektral schmalbandiger Dauerstrichlaser und eine Ionisation transversal zum frei propagierenden Atomstrahl ermöglicht durch Auflösung der Isotopieverschiebung eine hohe Selektivität gegenüber dominanten Nachbarisotopen, wohingegen die Ionisationseffizienz deutlich abnimmt. Hiermit konnte für das Ultraspurenisotop U-236 eine Nachweisgrenze bis hinab zu 10^-9 für das Isotopenverhältnis N(U-236)/N(U-238) bestimmt werden.

Charge-transport simulations in organic semiconductors

In this thesis we have extended the methods for microscopic charge-transport simulations for organic semiconductors. In these materials the weak intermolecular interactions lead to spatially localized charge carriers, and the charge transport occurs as an activated hopping process between diabatic states. In addition to weak electronic couplings between these states, different electrostatic environments in the organic material lead to a broadening of the density of states for the charge energies which limits carrier mobilities.rnThe contributions to the method development includern(i) the derivation of a bimolecular charge-transfer rate,rn(ii) the efficient evaluation of intermolecular (outer-sphere) reorganization energies,rn(iii) the investigation of effects of conformational disorder on intramolecular reorganization energies or internal site energiesrnand (iv) the inclusion of self-consistent polarization interactions for calculation of charge energies.These methods were applied to study charge transport in amorphous phases of small molecules used in the emission layer of organic light emitting diodes (OLED).rnWhen bulky substituents are attached to an aromatic core in order to adjust energy levels or prevent crystallization, a small amount of delocalization of the frontier orbital to the substituents can increase electronic couplings between neighboring molecules. This leads to improved charge-transfer rates and, hence, larger charge-mobility. We therefore suggest using the mesomeric effect (as opposed to the inductive effect) when attaching substituents to aromatic cores, which is necessary for example in deep blue OLEDs, where the energy levels of a host molecule have to be adjusted to those of the emitter.rnFurthermore, the energy landscape for charges in an amorphous phase cannot be predicted by mesoscopic models because they approximate the realistic morphology by a lattice and represent molecular charge distributions in a multipole expansion. The microscopic approach shows that a polarization-induced stabilization of a molecule in its charged and neutral states can lead to large shifts, broadening, and traps in the distribution of charge energies. These results are especially important for multi-component systems (the emission layer of an OLED or the donor-acceptor interface of an organic solar cell), if the change in polarizability upon charging (or excitation in case of energy transport) is different for the components. Thus, the polarizability change upon charging or excitation should be added to the set of molecular parameters essential for understanding charge and energy transport in organic semiconductors.rnWe also studied charge transport in self-assembled systems, where intermolecular packing motives induced by side chains can increase electronic couplings between molecules. This leads to larger charge mobility, which is essential to improve devices such as organic field effect transistors, where low carrier mobilities limit the switching frequency.rnHowever, it is not sufficient to match the average local molecular order induced by the sidernchains (such as the pitch angle between consecutive molecules in a discotic mesophase) with maxima of the electronic couplings.rnIt is also important to make the corresponding distributions as narrow as possible compared to the window determined by the closest minima of thernelectronic couplings. This is especially important in one-dimensional systems, where charge transport is limited by the smallest electronic couplings.rnThe immediate implication for compound design is that the side chains should assist the self-assemblingrnprocess not only via soft entropic interactions, but also via stronger specific interactions, such as hydrogen bonding.rnrnrnrn

Studies of degradation of organic solar cell materials using electrical scanning probe microscopy

Intense research is being done in the field of organic photovoltaics in order to synthesize low band-gap organic molecules. These molecules are electron donors which feature in combination with acceptor molecules, typically fullerene derivarntives, forming an active blend. This active blend has phase separated bicontinuous morphology on a nanometer scale. The highest recorded power conversionrnefficiencies for such cells have been 10.6%. Organic semiconductors differ from inorganic ones due to the presence of tightly bonded excitons (electron-hole pairs)resulting from their low dielectric constant (εr ≈2-4). An additional driving force is required to separate such Frenkel excitons since their binding energy (0.3-1 eV) is too large to be dissociated by an electric field alone. This additional driving force arises from the energy difference between the lowest unoccupied molecular orbital (LUMO) of the donor and the acceptor materials. Moreover, the efficiency of the cells also depends on the difference between the highest occupied molecular orbital (HOMO) of the donor and LUMO of the acceptor. Therefore, a precise control and estimation of these energy levels are required. Furthermore any external influences that change the energy levels will cause a degradation of the power conversion efficiency of organic solar cell materials. In particular, the role of photo-induced degradation on the morphology and electrical performance is a major contribution to degradation and needs to be understood on a nanometer scale. Scanning Probe Microscopy (SPM) offers the resolution to image the nanometer scale bicontinuous morphology. In addition SPM can be operated to measure the local contact potential difference (CPD) of materials from which energy levels in the materials can be derived. Thus SPM is an unique method for the characterization of surface morphology, potential changes and conductivity changes under operating conditions. In the present work, I describe investigations of organic photovoltaic materials upon photo-oxidation which is one of the major causes of degradation of these solar cell materials. SPM, Nuclear Magnetic Resonance (NMR) and UV-Vis spectroscopy studies allowed me to identify the chemical reactions occurring inside the active layer upon photo-oxidation. From the measured data, it was possible to deduce the energy levels and explain the various shifts which gave a better understanding of the physics of the device. In addition, I was able to quantify the degradation by correlating the local changes in the CPD and conductivity to the device characteristics, i.e., open circuit voltage and short circuit current. Furthermore, time-resolved electrostatic force microscopy (tr-EFM) allowed us to probe dynamic processes like the charging rate of the individual donor and acceptor domains within the active blend. Upon photo-oxidation, it was observed, that the acceptor molecules got oxidized first preventing the donor polymer from degrading. Work functions of electrodes can be tailored by modifying the interface with monomolecular thin layers of molecules which are made by a chemical reaction in liquids. These modifications in the work function are particularly attractive for opto-electronic devices whose performance depends on the band alignment between the electrodes and the active material. In order to measure the shift in work function on a nanometer scale, I used KPFM in situ, which means in liquids, to follow changes in the work function of Au upon hexadecanethiol adsorption from decane. All the above investigations give us a better understanding of the photo-degradation processes of the active material at the nanoscale. Also, a method to compare various new materials used for organic solar cells for stability is proposed which eliminates the requirement to make fully functional devices saving time and additional engineering efforts.

Elementspeziation von Neptunium im Ultraspurenbereich

In der vorliegenden Arbeit wurde der Nachweis des Isotops Np-237 mit Resonanzionisations-Massenspektrometrie (RIMS) entwickelt und optimiert. Bei RIMS werden Probenatome mehrstufig-resonant mit Laserstrahlung angeregt, ionisiert und anschließend massenspektrometrisch nachgewiesen. Die Bestimmung geeigneter Energiezustände für die Anregung und Ionisation von Np-237 erfolgte durch Resonanzionisationsspektroskopie (RIS), wobei über 300 bisher unbekannte Energieniveaus und autoionisierende Zustände von Np-237 identifiziert wurden. Mit in-source-RIMS wird für das Isotop eine Nachweisgrenze von 9E+5 Atome erreicht. rnrnDie Mobilität von Np in der Umwelt hängt stark von seiner Elementspeziation ab. Für Sicherheitsanalysen potentieller Endlagerstandorte werden daher Methoden benötigt, die Aussagen über die unter verschiedenen Bedingungen vorliegenden Neptuniumspezies ermöglichen. Hierzu wurde eine online-Kopplung aus Kapillarelektrophorese (CE) und ICP-MS (inductively coupled plasma mass spectrometry) genutzt, mit der die Np-Redoxspezies Np(IV) und Np(V) noch bei einer Konzentrationen von 1E-9 mol/L selektiv nachgewiesen werden können. Das Verfahren wurde eingesetzt, um die Wechselwirkung des Elements mit Opalinuston unter verschiedenen Bedingungen zu untersuchen. Dabei konnte gezeigt werden, dass bei Gegenwart von Fe(II) Np(V) zu Np(IV) reduziert wird und dieses am Tongestein sorbiert. Dies führt insgesamt zu einer deutlich erhöhten Sorption des Np am Ton.

Light harvesting and orbital tuning : perylene monoimides and diimides for photovoltaic purposes

Die vorliegende Dissertation beschaftigt sich mit der Steuerung der Absorption und Orbitalenergien von Perylenmonoimiden und Perylendiimiden fur die Anwendung in organischer Photovoltaik (OPV). Eine breite Absorption spielt hier eine wichtige Rolle, um moglichst viel Licht zu ernten, das dann in elektrische Energie umgewandelt wird. Um sicher zu stellen, dass die Zelle ezient arbeiten kann, ist die Abstimmung von Orbitalenergien eine zweite wichtige Voraussetzung. Es werden drei neue Design-Konzepte fur Perylenmonoimid-Sensibilatoren fur Festk orper-Farbstosolarzellen (solid-state dye-sensitised solar cells - sDSSCs) untersucht. Die Synthese, die optischen und elektronischen Eigenschaften der neuen Sensibilisator- Verbindungen sowie ihre Leistungsdaten in sDSSCs werden beschrieben und diskutiert. Die in dieser Arbeit vorgestellten Konzepte reichen von der Einfuhrung von - Abstandhaltern uber neue Funktionalisierungen bis hin zur Erweiterung der Perylenmonimid Grundkorper. Der Push-Pull-Charakter der Systeme variiert von starker Kopplung bis zu kompletter Entkopplung des Donors vom Akzeptor. Dies hat einen starken Ein uss sowohl auf die Absorptionseigenschaften, als auch auf die HOMO/LUMO Energie-Niveaus der Verbindungen. Einige der Konzepte konnen auf Perylendiimide ubertragen werden. Ein Beispiel von Perylendiimid (PDI)-Farbsteuerung wird an einer Reihe von drei Terthiophen-PDIs gezeigt

Novel organic semiconductors and their applications in electronics

The main goals of this thesis were the design, synthesis, and characterization of novel organic semiconductors, together with their applications in electronics, such as OFETs, OPVs, and OLEDs. The results can be summarized as follows:rn1. In chapter II, two novel angular n-type molecules were presented. Their different alkyl chains play a pivotal role in the molecular orientation relative to surface. One molecule with longer branched chains is tilted with respect to the substrate, thereby resulting in poor device performance, while the other adopt an edge-on orientation with an OFET electron mobility of 0.01 cm2 V-1 s-1.rn2. In chapter III, fused bis-benzothiadiazoles with different molecular geometries, namely linear benzoquinone-fused bis(benzothiadiazole) and V-shaped sulfone-fused bis(benzothiadiazole), were shown. This work not only contributes to the diversity of electron acceptors based on bis-benzothiadiazole moieties, but also highlights the important role of molecular shape for the solid-state packing of organic conjugated materials. In chapter IV, we demonstrated the synthesis of layered acceptors via dimerization of thiadiazole end-capped acenes. Interestingly, they feature huge differences in their photophysical properties. One compound showed a new strong emission in the near-infrared region introduced by the aggregation effect. The planosymmetric compound featured intramolecular excimer (IEE) fluorescence in solution. rn3. In chapter V and VI, we have demonstrated the synthesis of novel spiro-bifluorene based asymmetric and symmetric cruciform electron acceptors with dicyanovinylene substitutions. The solar cells based on PTB7:asymmetric acceptor yields the highest PCE of 0.80%. Such results demonstrate for the first time that dicyanovinylene substituted acceptor could be an alternative to fullerene-based acceptors. rn4. In chapter VII, two novel blue-emitting compounds were shown, which consist of dihydroindenofluorenyl units and ladder-type poly-p-phenylene groups, respectively. The two novel cruciform rigid compounds present not only excellent thermal and electrochemical stability but also high PLQYs. Through analysis of their triplet energy levels, both molecules can be served as hosts for other normal fluorescent or phosphorescent materials.rn

Planck stars: theory and phenomenology

General Relativity (GR) is one of the greatest scientific achievements of the 20th century along with quantum theory. Despite the elegance and the accordance with experimental tests, these two theories appear to be utterly incompatible at fundamental level. Black holes provide a perfect stage to point out these difficulties. Indeed, classical GR fails to describe Nature at small radii, because nothing prevents quantum mechanics from affecting the high curvature zone, and because classical GR becomes ill-defined at r = 0 anyway. Rovelli and Haggard have recently proposed a scenario where a negative quantum pressure at the Planck scales stops and reverts the gravitational collapse, leading to an effective “bounce” and explosion, thus resolving the central singularity. This scenario, called Black Hole Fireworks, has been proposed in a semiclassical framework. The purpose of this thesis is twofold: - Compute the bouncing time by means of a pure quantum computation based on Loop Quantum Gravity; - Extend the known theory to a more realistic scenario, in which the rotation is taken into account by means of the Newman-Janis Algorithm.

Atmospheric Implications for Formation of Clusters of Ammonium and 1−10 Water Molecules

A mixed molecular dynamics/quantum mechanics model has been applied to the ammonium/water clustering system. The use of the high level MP2 calculation method and correlated basis sets, such as aug-cc-pVDZ and aug-cc-pVTZ, lends confidence in the accuracy of the extrapolated energies. These calculations provide electronic and free energies for the formation of clusters of ammonium and 1−10 water molecules at two different temperatures. Structures and thermodynamic values are in good agreement with previous experimental and theoretical results. The estimated concentration of these clusters in the troposphere was calculated using atmospheric amounts of ammonium and water. Results show the favorability of forming these clusters and implications for ion-induced nucleation in the atmosphere.

Minimal assumption derivation of a weak Clauser-Horne inequality

According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality (LC) conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of LC, yet assuming the existence of perfectly correlated event types. Here we present a similar Bell-type theorem without this latter assumption. The derived inequality differs from the Clauser-Horne inequality by some small correction terms, which render it less constraining.

Arc-flash analysis of utility power systems

The electric utility business is an inherently dangerous area to work in with employees exposed to many potential hazards daily. One such hazard is an arc flash. An arc flash is a rapid release of energy, referred to as incident energy, caused by an electric arc. Due to the random nature and occurrence of an arc flash, one can only prepare and minimize the extent of harm to themself, other employees and damage to equipment due to such a violent event. Effective January 1, 2009 the National Electric Safety Code (NESC) requires that an arc-flash assessment be performed by companies whose employees work on or near energized equipment to determine the potential exposure to an electric arc. To comply with the NESC requirement, Minnesota Power’s (MP’s) current short circuit and relay coordination software package, ASPEN OneLinerTM and one of the first software packages to implement an arc-flash module, is used to conduct an arc-flash hazard analysis. At the same time, the package is benchmarked against equations provided in the IEEE Std. 1584-2002 and ultimately used to determine the incident energy levels on the MP transmission system. This report goes into the depth of the history of arc-flash hazards, analysis methods, both software and empirical derived equations, issues of concern with calculation methods and the work conducted at MP. This work also produced two offline software products to conduct and verify an offline arc-flash hazard analysis.

Stochastic rank correlation: a robust merit function for 2D/3D registration of image data obtained at different energies

In this article, the authors evaluate a merit function for 2D/3D registration called stochastic rank correlation (SRC). SRC is characterized by the fact that differences in image intensity do not influence the registration result; it therefore combines the numerical advantages of cross correlation (CC)-type merit functions with the flexibility of mutual-information-type merit functions. The basic idea is that registration is achieved on a random subset of the image, which allows for an efficient computation of Spearman's rank correlation coefficient. This measure is, by nature, invariant to monotonic intensity transforms in the images under comparison, which renders it an ideal solution for intramodal images acquired at different energy levels as encountered in intrafractional kV imaging in image-guided radiotherapy. Initial evaluation was undertaken using a 2D/3D registration reference image dataset of a cadaver spine. Even with no radiometric calibration, SRC shows a significant improvement in robustness and stability compared to CC. Pattern intensity, another merit function that was evaluated for comparison, gave rather poor results due to its limited convergence range. The time required for SRC with 5% image content compares well to the other merit functions; increasing the image content does not significantly influence the algorithm accuracy. The authors conclude that SRC is a promising measure for 2D/3D registration in IGRT and image-guided therapy in general.

Modern charge density studies: the entanglement of experiment and theory

This tutorial review article is intended to provide a general guidance to a reader interested to learn about the methodologies to obtain accurate electron density mapping in molecules and crystalline solids, from theory or from experiment, and to carry out a sensible interpretation of the results, for chemical, biochemical or materials science applications. The review mainly focuses on X-ray diffraction techniques and refinement of experimental models, in particular multipolar models. Neutron diffraction, which was widely used in the past to fix accurate positions of atoms, is now used for more specific purposes. The review illustrates three principal analyses of the experimental or theoretical electron density, based on quantum chemical, semi-empirical or empirical interpretation schemes, such as the quantum theory of atoms in molecules, the semi-classical evaluation of interaction energies and the Hirshfeld analysis. In particular, it is shown that a simple topological analysis based on a partition of the electron density cannot alone reveal the whole nature of chemical bonding. More information based on the pair density is necessary. A connection between quantum mechanics and observable quantities is given in order to provide the physical grounds to explain the observations and to justify the interpretations.