New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Quantum hydrodynamic models for semiconductors with and without collisions

In dieser Arbeit werden Quantum-Hydrodynamische (QHD) Modelle betrachtet, die ihren Einsatz besonders in der Modellierung von Halbleiterbauteilen finden. Das QHD Modell besteht aus den Erhaltungsgleichungen für die Teilchendichte, das Momentum und die Energiedichte, inklusive der Quanten-Korrekturen durch das Bohmsche Potential. Zu Beginn wird eine Übersicht über die bekannten Ergebnisse der QHD Modelle unter Vernachlässigung von Kollisionseffekten gegeben, die aus ein­em Schrödinger-System für den gemischten-Zustand oder aus der Wigner-Glei­chung hergeleitet werden können. Nach der Reformulierung der eindimensionalen QHD Gleichungen mit linearem Potential als stationäre Schrö­din­ger-Gleichung werden die semianalytischen Fassungen der QHD Gleichungen für die Gleichspannungs-Kurve betrachtet. Weiterhin werden die viskosen Stabilisierungen des QHD Modells be­rück­sich­tigt, sowie die von Gardner vorgeschlagene numerische Viskosität für das {sf upwind} Finite-Differenzen Schema berechnet. Im Weiteren wird das viskose QHD Modell aus der Wigner-Glei­chung mit Fokker-Planck Kollisions-Ope­ra­tor hergeleitet. Dieses Modell enthält die physikalische Viskosität, die durch den Kollision-Operator eingeführt wird. Die Existenz der Lösungen (mit strikt positiver Teilchendichte) für das isotherme, stationäre, eindimensionale, viskose Modell für allgemeine Daten und nichthomogene Randbedingungen wird gezeigt. Die dafür notwendigen Abschätzungen hängen von der Viskosität ab und erlauben daher den Grenzübergang zum nicht-viskosen Fall nicht. Numerische Simulationen der Resonanz-Tunneldiode modelliert mit dem nichtisothermen, stationären, eindimensionalen, viskosen QHD Modell zeigen den Einfluss der Viskosität auf die Lösung. Unter Verwendung des von Degond und Ringhofer entwickelten Quanten-Entropie-Minimierungs-Verfahren werden die allgemeinen QHD-Gleichungen aus der Wigner-Boltzmann-Gleichung mit dem BGK-Kollisions-Operator hergeleitet. Die Herleitung basiert auf der vorsichtige Entwicklung des Quanten-Max­well­ians in Potenzen der skalierten Plankschen Konstante. Das so erhaltene Modell enthält auch vertex-Terme und dispersive Terme für die Ge­schwin­dig­keit. Dadurch bleibt die Gleichspannungs-Kurve für die Re­so­nanz-Tunnel­diode unter Verwendung des allgemeinen QHD Modells in einer Dimension numerisch erhalten. Die Ergebnisse zeigen, dass der dispersive Ge­schwin­dig­keits-Term die Lösung des Systems stabilisiert.

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Quantum dot-dye hybrid systems for energy transfer applications

In this thesis, we focus on the preparation of energy transfer-based quantum dot (QD)-dye hybrid systems. Two kinds of QD-dye hybrid systems have been successfully synthesized: QD-silica-dye and QD-dye hybrid systems.rn rnIn the QD-silica-dye hybrid system, multishell CdSe/CdS/ZnS QDs were adsorbed onto monodisperse Stöber silica particles with an outer silica shell of thickness 2 - 24 nm containing organic dye molecules (Texas Red). The thickness of this dye layer has a strong effect on the total sensitized acceptor emission, which is explained by the increase in the number of dye molecules homogeneously distributed within the silica shell, in combination with an enhanced surface adsorption of QDs with increasing dye amount. Our conclusions were underlined by comparison of the experimental results with Monte-Carlo simulations, and by control experiments confirming attractive interactions between QDs and Texas Red freely dissolved in solution. rnrnNew QD-dye hybrid system consisting of multishell QDs and organic perylene dyes have been synthesized. We developed a versatile approach to assemble extraordinarily stable QD-dye hybrids, which uses dicarboxylate anchors to bind rylene dyes to QD. This system yields a good basis to study the energy transfer between QD and dye because of its simple and compact design: there is no third kind of molecule linking QD and dye; no spacer; and the affinity of the functional group to the QD surface is strong. The FRET signal was measured for these complexes as a function of both dye to QD ratio and center-to-center distance between QD and dye by controlling number of covered ZnS layers. Data showed that fluorescence resonance energy transfer (FRET) was the dominant mechanism of the energy transfer in our QD-dye hybrid system. FRET efficiency can be controlled by not only adjusting the number of dyes on the QD surface or the QD to dye distance, but also properly choosing different dye and QD components. Due to the strong stability, our QD-dye complexes can also be easily transferred into water. Our approach can apply to not only dye molecules but also other organic molecules. As an example, the QDs have been complexed with calixarene molecules and the QD-calixarene complexes also have potential for QD-based energy transfer study. rn

A scanning electron microscope for ultracold quantum gases

This thesis presents a new imaging technique for ultracold quantum gases. Since the first observation of Bose-Einstein condensation, ultracold atoms have proven to be an interesting system to study fundamental quantum effects in many-body systems. Most of the experiments use optical imaging rnmethods to extract the information from the system and are therefore restricted to the fundamental limitation of this technique: the best achievable spatial resolution that can be achieved is comparable to the wavelength of the employed light field. Since the average atomic distance and the length scale of characteristic spatial structures in Bose-Einstein condensates such as vortices and solitons is between 100 nm and 500 nm, an imaging technique with an adequate spatial resolution is needed. This is achieved in this work by extending the method of scanning electron microscopy to ultracold quantum gases. A focused electron beam is scanned over the atom cloud and locally produces ions which are subsequently detected. The new imaging technique allows for the precise measurement of the density distribution of a trapped Bose-Einstein condensate. Furthermore, the spatial resolution is determined by imaging the atomic distribution in one-dimensional and two-dimensional optical lattices. Finally, the variety of the imaging method is demonstrated by the selective removal of single lattice site. rn

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

Coarse-graining and quantum-classical adaptive coupling in soft matter

Die vorliegende Arbeit untersucht den Zusammenhang zwischen Skalen in Systemen weicher Materie, der für Multiskalen-Simulationen eine wichtige Rolle spielt. Zu diesem Zweck wurde eine Methode entwickelt, die die Approximation der Separierbarkeit von Variablen für die Molekulardynamik und ähnliche Anwendungen bewertet. Der zweite und größere Teil dieser Arbeit beschäftigt sich mit der konzeptionellen und technischen Erweiterung des Adaptive Resolution Scheme'' (AdResS), einer Methode zur gleichzeitigen Simulation von Systemen mit mehreren Auflösungsebenen. Diese Methode wurde auf Systeme erweitert, in denen klassische und quantenmechanische Effekte eine Rolle spielen.rnrnDie oben genannte erste Methode benötigt nur die analytische Form der Potentiale, wie sie die meisten Molekulardynamik-Programme zur Verfügung stellen. Die Anwendung der Methode auf ein spezielles Problem gibt bei erfolgreichem Ausgang einen numerischen Hinweis auf die Gültigkeit der Variablenseparation. Bei nicht erfolgreichem Ausgang garantiert sie, dass keine Separation der Variablen möglich ist. Die Methode wird exemplarisch auf ein zweiatomiges Molekül auf einer Oberfläche und für die zweidimensionale Version des Rotational Isomer State (RIS) Modells einer Polymerkette angewandt.rnrnDer zweite Teil der Arbeit behandelt die Entwicklung eines Algorithmus zur adaptiven Simulation von Systemen, in denen Quanteneffekte berücksichtigt werden. Die Quantennatur von Atomen wird dabei in der Pfadintegral-Methode durch einen klassischen Polymerring repräsentiert. Die adaptive Pfadintegral-Methode wird zunächst für einatomige Flüssigkeiten und tetraedrische Moleküle unter normalen thermodynamischen Bedingungen getestet. Schließlich wird die Stabilität der Methode durch ihre Anwendung auf flüssigen para-Wasserstoff bei niedrigen Temperaturen geprüft.

Interacting fermionic atoms in optical lattices - A quantum simulator for condensed matter physics

This thesis reports on the creation and analysis of many-body states of interacting fermionic atoms in optical lattices. The realized system can be described by the Fermi-Hubbard hamiltonian, which is an important model for correlated electrons in modern condensed matter physics. In this way, ultra-cold atoms can be utilized as a quantum simulator to study solid state phenomena. The use of a Feshbach resonance in combination with a blue-detuned optical lattice and a red-detuned dipole trap enables an independent control over all relevant parameters in the many-body hamiltonian. By measuring the in-situ density distribution and doublon fraction it has been possible to identify both metallic and insulating phases in the repulsive Hubbard model, including the experimental observation of the fermionic Mott insulator. In the attractive case, the appearance of strong correlations has been detected via an anomalous expansion of the cloud that is caused by the formation of non-condensed pairs. By monitoring the in-situ density distribution of initially localized atoms during the free expansion in a homogeneous optical lattice, a strong influence of interactions on the out-of-equilibrium dynamics within the Hubbard model has been found. The reported experiments pave the way for future studies on magnetic order and fermionic superfluidity in a clean and well-controlled experimental system.

Interacting quantum-dissipative tunnelling systems

Die Untersuchung von dissipativen Quantensystemen erm¨oglicht es, Quantenph¨anomene auch auf makroskopischen L¨angenskalen zu beobachten. Das in dieser Dissertation gew¨ahlte mikroskopische Modell erlaubt es, den bisher nur ph¨anomenologisch zug¨anglichen Effekt der Quantendissipation mathematisch und physikalisch herzuleiten und zu untersuchen. Bei dem betrachteten mikroskopischen Modell handelt es sich um eine 1-dimensionale Kette von harmonischen Freiheitsgraden, die sowohl untereinander als auch an r anharmonische Freiheitsgrade gekoppelt sind. Die F¨alle einer, respektive zwei anharmonischer Bindungen werden in dieser Arbeit explizit betrachtet. Hierf¨ur wird eine analytische Trennung der harmonischen von den anharmonischen Freiheitsgraden auf zwei verschiedenen Wegen durchgef¨uhrt. Das anharmonische Potential wird als symmetrisches Doppelmuldenpotential gew¨ahlt, welches mit Hilfe der Wick Rotation die Berechnung der ¨Uberg¨ange zwischen beiden Minima erlaubt. Das Eliminieren der harmonischen Freiheitsgrade erfolgt mit Hilfe des wohlbekannten Feynman-Vernon Pfadintegral-Formalismus [21]. In dieser Arbeit wird zuerst die Positionsabh¨angigkeit einer anharmonischen Bindung im Tunnelverhalten untersucht. F¨ur den Fall einer fernab von den R¨andern lokalisierten anharmonischen Bindung wird ein Ohmsches dissipatives Tunneln gefunden, was bei der Temperatur T = 0 zu einem Phasen¨ubergang in Abh¨angigkeit einer kritischen Kopplungskonstanten Ccrit f¨uhrt. Dieser Phasen¨ubergang wurde bereits in rein ph¨anomenologisches Modellen mit Ohmscher Dissipation durch das Abbilden des Systems auf das Ising-Modell [26] erkl¨art. Wenn die anharmonische Bindung jedoch an einem der R¨ander der makroskopisch grossen Kette liegt, tritt nach einer vom Abstand der beiden anharmonischen Bindungen abh¨angigen Zeit tD ein ¨Ubergang von Ohmscher zu super- Ohmscher Dissipation auf, welche im Kern KM(τ ) klar sichtbar ist. F¨ur zwei anharmonische Bindungen spielt deren indirekteWechselwirkung eine entscheidende Rolle. Es wird gezeigt, dass der Abstand D beider Bindungen und die Wahl des Anfangs- und Endzustandes die Dissipation bestimmt. Unter der Annahme, dass beide anharmonischen Bindung gleichzeitig tunneln, wird eine Tunnelwahrscheinlichkeit p(t) analog zu [14], jedoch f¨ur zwei anharmonische Bindungen, berechnet. Als Resultat erhalten wir entweder Ohmsche Dissipation f¨ur den Fall, dass beide anharmonischen Bindungen ihre Gesamtl¨ange ¨andern, oder super-Ohmsche Dissipation, wenn beide anharmonischen Bindungen durch das Tunneln ihre Gesamtl¨ange nicht ¨andern.

The g-factor of the electron bound in 28 Si 13+ : the most stringent test of bound-state quantum electrodynamics

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike 28Si13+. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision.rnThe development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 40 ppt, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.

Biologischer Lichtsammler (LHCII) für Halbleiternanokristalle (Quantum Dots)

Der light harvesting complex II (LHCII) ist ein pflanzliches Membranprotein, das in seiner trimeren Form über 40 Chlorophylle bindet. In der Pflanze kann er besonders effizient Licht sammeln und die Anregungsenergie anschließend fast verlustfrei über andere chlorophyll-bindende Proteine an die Reaktionszentren weiterleiten. Aufgrund dieser besonderen Eigenschaften war es ein Ziel dieser Arbeit, rekombinanten LHCII mit synthetischen Komponenten zu kombinieren, die zur Ladungstrennung befähigt sind. Zu diesem Zweck wurden unter anderem Halbleiternanokristalle (Quantum Dots, QDs) ausgewählt, die je nach Zusammensetzung sowohl als Energieakzeptoren als auch als Energiedonoren in Frage kamen. Durch Optimierung des Puffers gelang es, die Fluoreszenzquantenausbeute der QDs in wässriger Lösung zu erhöhen und zu stabilisieren, so dass die Grundvoraussetzungen für die spektroskopische Untersuchung verschiedener LHCII-QD-Hybridkomplexe erfüllt waren.rnUnter Verwendung bereits etablierter Affinitätssequenzen zur Bindung des LHCII an die QDs konnte gezeigt werden, dass die in dieser Arbeit verwendeten Typ-I QDs aus CdSe und ZnS sich kaum als Energie-Donoren für den LHCII eignen. Ein Hauptgrund lag im vergleichsweise kleinen Försterradius R0 von 4,1 nm. Im Gegensatz dazu wurde ein R0 von 6,4 nm für den LHCII als Donor und Typ-II QDs aus CdTe, CdSe und ZnS als Akzeptor errechnet, wodurch in diesem System eine höhere Effizienz des Energietransfers zu erwarten war. Fluoreszenzspektroskopische Untersuchungen von Hybridkomplexen aus LHCII und Typ-II QDs ergaben eine hohe Plausibilität für einen Fluoreszenz Resonanz Energietransfer (FRET) vom Lichtsammler auf die QDs. Weitere QD-Affinitätssequenzen für den LHCII wurden identifiziert und deren Bindekonstanten ermittelt. Versuche mit dem Elektronenakzeptor Methylviologen lieferten gute Hinweise auf eine LHCII-sensibilisierte Ladungstrennung der Typ-II QDs, auch wenn dies noch anhand alternativer Messmethoden wie z.B. durch transiente Absorptionsspektroskopie bestätigt werden muss. rnEin weiteres Ziel war die Verwendung von LHCII als Lichtsammler in dye-sensitized solar cells (DSSC). Geeignete dotierte TiO2-Platten wurden ermittelt, das Verfahren zur Belegung der Platten optimiert und daher mit wenig Aufwand eine hohe LHCII-Belegungsdichte erzielt. Erste Messungen von Aktionsspektren mit LHCII und einem zur Ladungstrennung fähigen Rylenfarbstoff zeigen eine, wenn auch geringe, LHCII sensibilisierte Ladungstrennung. rnDie Verwendung von Lanthanide-Binding-Tags (LBTs) ist ein potentielles Verfahren zur in vivo-Markierung von Proteinen mit Lanthanoiden wie Europium und Terbium. Diese Metalle besitzen eine überdurchschnittlich lange Lumineszenzlebensdauer, so dass sie leicht von anderen fluoreszierenden Molekülen unterschieden werden können. Im Rahmen der vorliegenden Arbeit gelang es, eine LBT in rekombinanten LHCII einzubauen und einen Lumineszenz Resonanz Energietransfer (LRET) vom Europium auf den LHCII nachzuweisen.rn