Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.

Investigation of P3HT PCBM particle-based solar cells

Die Herstellung von Polymer-Solarzellen aus wässriger Phase stellt eine attraktive Alternative zu der konventionellen lösemittelbasierten Formulierung dar. Die Vorteile der aus wässriger Lösung hergestellten Solarzellen liegen besonders in dem umweltschonenden Herstellungsprozess und in der Möglichkeit, druckbare optoelektronische Bauteile zu generieren. Die Prozessierbarkeit von hydrophoben Halbleitern im wässrigen Milieu wird durch die Dispergierung der Materialien, in Form von Nanopartikeln, erreicht. Der Transfer der Halbleiter in eine Dispersion erfolgt über die Lösemittelverdampfungsmethode. Die Idee der Verwendung von partikelbasierte Solarzellen wurde bereits umgesetzt, allerdings blieben eine genaue Charakterisierung der Partikel sowie ein umfassendes Verständnis des gesamten Fabrikationsvorgangs aus. Deshalb besteht das Ziel dieser Arbeit darin, einen detaillierten Einblick in den Herstellungsprozess von partikelbasierten Solarzellen zu erlangen, mögliche Schwächen aufzudecken, diese zu beseitigen, um so zukünftige Anwendungen zu verbessern. Zur Herstellung von Solarzellen aus wässrigen Dispersionen wurde Poly(3-hexylthiophen-2,5-diyl)/[6,6]-Phenyl-C61-Buttersäure-Methylester (P3HT/PCBM) als Donor/Akzeptor-System verwendet. Die Kernpunkte der Untersuchungen richteten sich zum einen die auf Partikelmorphologie und zum anderen auf die Generierung einer geeigneten Partikelschicht. Beide Parameter haben Auswirkungen auf die Solarzelleneffizienz. Die Morphologie wurde sowohl spektroskopisch über Photolumineszenz-Messungen, als auch visuell mittels Elektronenmikroskopie ermittelt. Auf diese Weise konnte die Partikelmorphologie vollständig aufgeklärt werden, wobei Parallelen zu der Struktur von lösemittelbasierten Solarzellen gefunden wurden. Zudem wurde eine Abhängigkeit der Morphologie von der Präparationstemperatur beobachtet, was eine einfache Steuerung der Partikelstruktur ermöglicht. Im Zuge der Partikelschichtausbildung wurden direkte sowie grenzflächenvermittelnde Beschichtungsmethoden herangezogen. Von diesen Techniken hatte sich aber nur die Rotationsbeschichtung als brauchbare Methode erwiesen, Partikel aus der Dispersion in einen homogenen Film zu überführen. Des Weiteren stand die Aufarbeitung der Partikelschicht durch Ethanol-Waschung und thermische Behandlung im Fokus dieser Arbeit. Beide Maßnahmen wirkten sich positiv auf die Effizienz der Solarzellen aus und trugen entscheidend zu einer Verbesserung der Zellen bei. Insgesamt liefern die gewonnen Erkenntnisse einen detaillierten Überblick über die Herausforderungen, welche bei dem Einsatz von wasserbasierten Dispersionen auftreten. Die Anforderungen partikelbasierter Solarzellen konnten offengelegt werden, dadurch gelang die Herstellung einer Solarzelle mit einer Effizienz von 0.53%. Dieses Ergebnis stellt jedoch noch nicht das Optimum dar und lässt noch Möglichkeiten für Verbesserungen offen.

Convergence results for stochastic particle systems with social interaction

We consider stochastic individual-based models for social behaviour of groups of animals. In these models the trajectory of each animal is given by a stochastic differential equation with interaction. The social interaction is contained in the drift term of the SDE. We consider a global aggregation force and a short-range repulsion force. The repulsion range and strength gets rescaled with the number of animals N. We show that for N tending to infinity stochastic fluctuations disappear and a smoothed version of the empirical process converges uniformly towards the solution of a nonlinear, nonlocal partial differential equation of advection-reaction-diffusion type. The rescaling of the repulsion in the individual-based model implies that the corresponding term in the limit equation is local while the aggregation term is non-local. Moreover, we discuss the effect of a predator on the system and derive an analogous convergence result. The predator acts as an repulsive force. Different laws of motion for the predator are considered.

Probing quantum chromodynamics with the ATLAS detector : charged-particle event shape variables and the dijet cross-section

Die Quantenchromodynamik ist die zugrundeliegende Theorie der starken Wechselwirkung und kann in zwei Bereiche aufgeteilt werden. Harte Streuprozesse, wie zum Beispiel die Zwei-Jet-Produktion bei hohen invarianten Massen, können störungstheoretisch behandelt und berechnet werden. Bei Streuprozessen mit niedrigen Impulsüberträgen hingegen ist die Störungstheorie nicht mehr anwendbar und phänemenologische Modelle werden für Vorhersagen benutzt. Das ATLAS Experiment am Large Hadron Collider am CERN ermöglicht es, QCD Prozesse bei hohen sowie niedrigen Impulsüberträgen zu untersuchen. In dieser Arbeit werden zwei Analysen vorgestellt, die jeweils ihren Schwerpunkt auf einen der beiden Regime der QCD legen:rnDie Messung von Ereignisformvariablen bei inelastischen Proton--Proton Ereignissen bei einer Schwerpunktsenergie von $sqrt{s} = unit{7}{TeV}$ misst den transversalen Energiefluss in hadronischen Ereignissen. rnDie Messung des zweifachdifferentiellen Zwei-Jet-Wirkungsquerschnittes als Funktion der invarianten Masse sowie der Rapiditätsdifferenz der beiden Jets mit den höchsten Transversalimpulsen kann genutzt werden um Theorievorhersagen zu überprüfen. Proton--Proton Kollisionen bei $sqrt{s} = unit{8}{TeV}$, welche während der Datennahme im Jahr 2012 aufgezeichnet wurden, entsprechend einer integrierten Luminosität von $unit{20.3}{fb^{-1}}$, wurden analysiert.rn

Fast frontend electronics for high rate particle detectors

Future experiments in nuclear and particle physics are moving towards the high luminosity regime in order to access rare processes. In this framework, particle detectors require high rate capability together with excellent timing resolution for precise event reconstruction. In order to achieve this, the development of dedicated FrontEnd Electronics (FEE) for detectors has become increasingly challenging and expensive. Thus, a current trend in R&D is towards flexible FEE that can be easily adapted to a great variety of detectors, without impairing the required high performance. This thesis reports on a novel FEE for two different detector types: imaging Cherenkov counters and plastic scintillator arrays. The former requires high sensitivity and precision for detection of single photon signals, while the latter is characterized by slower and larger signals typical of scintillation processes. The FEE design was developed using high-bandwidth preamplifiers and fast discriminators which provide Time-over-Threshold (ToT). The use of discriminators allowed for low power consumption, minimal dead-times and self-triggering capabilities, all fundamental aspects for high rate applications. The output signals of the FEE are readout by a high precision TDC system based on FPGA. The performed full characterization of the analogue signals under realistic conditions proved that the ToT information can be used in a novel way for charge measurements or walk corrections, thus improving the obtainable timing resolution. Detailed laboratory investigations proved the feasibility of the ToT method. The full readout chain was investigated in test experiments at the Mainz Microtron: high counting rates per channel of several MHz were achieved, and a timing resolution of better than 100 ps after walk correction based on ToT was obtained. Ongoing applications to fast Time-of-Flight counters and future developments of FEE have been also recently investigated.