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.

The influence of heat treatment on the phase relations in mineral growth systems

ABSTRACT Corundum is one of the most famous gems materials. Different heat treatment methods for enhancement purposes are commonly applied and accepted in the gem market. With this reason, the identification of the natural, unheated corundum is intensively investigated. In this study, aluminium hydroxide minerals and zircon are focused to observe the crystallization and phase change of these minerals during heat treatment procedures. Aluminium hydroxide minerals can be transformed to alumina with the corundum structure by heating. The reaction history of aluminium hydroxide minerals containing corundum was investigated comparing it with diaspore, boehmite, gibbsite and bayerite by TG and DTA methods. These hydroxide minerals were entirely transformed to corundum after heating at 600°C. Zircon inclusions in corundums from Ilakaka, Madagascar, were investigated for the influence of different heat-treatment temperatures on the recovery of their crystalline structure and on possible reactions within and with the host crystals. The host corundum was heated at 500, 800, 1000, 1200, 1400, 1600 and 1800°C. The crystallinity, the trapped pressure, and the decomposition of the zircon inclusions within the host corundum have been investigated by Raman spectroscopy. Radiation-damaged zircon inclusions may be used as an indicator for unheated Ilakaka corundum crystals. They are fully recrystallized after heating at 1000°C influencing the lowering of the 3 Raman band shift, the decreasing of FWHM of the 3 Raman band and the decreasing of the trapped pressure between the inclusion and the host corundum. Under microscopic observation, surface alterations of the inclusions can be firstly seen from transparent into frosted-like appearance at 1400°C. Then, between 1600°C and 1800 °C, the inclusion becomes partly or even completely molten. The decomposition of the zircon inclusion to m-ZrO2 and SiO2-glass phases begins at the rim of the inclusion after heating from 1200°C to 1600°C which can be detected by the surface change, the increase of the 3 Raman band position and the trapped pressure. At 1800°C, the zircon inclusions entirely melt transforming to solid phases during cooling like m-ZrO2 and SiO2-glass accompanied by an increase of pressure between the transformed inclusion and its host.

RAB3GAP1 und RAB3GAP2 (RAB3 GTPase-activating Protein 1/2) beeinflussen die Autophagie in C. elegans und humanen Zellen

Die Proteinhomöostase wird in der Zelle von drei Stoffwechselwegen reguliert: den molekularen Chaperonen, dem Ubiquitin-Proteasom-System und dem autophagosomalen Abbauweg. Die (Makro)Autophagie verpackt und transportiert zytosolische Komponenten in Autophagosomen zu den Lysosomen, wo sie abgebaut werden. Eine Störung dieses Abbauwegs wirkt auf die Proteostase.rnIn dieser Dissertation wurde C. elegans als Modellorganismus zur Erforschung von Proteinstabilität genutzt. In einer RNAi-vermittelten Proteostase-Analyse von Chromosom I und ausgewählter zusätzlicher Gene wurde ein Wurmstamm, der ein Luc::GFP-Konstrukt im Muskel exprimiert, genutzt. Dieses Reporterprotein aggregiert unter Hitzestressbedingungen und diese Aggregation kann durch Modulatoren der Proteostase beeinflusst werden. Dabei wurden mögliche neue Faktoren der Proteinhomöostase entdeckt. Durch weitere Experimente bei denen die Aggregation von PolyQ35::YFP im AM140-System, der Paralyse-Phänotyp und die Akkumulation Thioflavin S-gefärbter Aggregate von Aβ42 im CL2006-Wurmstamm und die Effekte auf die Autophagie mittels eines GFP::LGG1-Konstrukt analysiert wurden, konnten rbg-1 und rbg-2 als neue Modulatoren der Proteinhomöostase, insbesondere der Autophagie, identifiziert werden.rnIm Säuger bilden beide Orthologe dieser Gene, RAB3GAP1 und RAB3GAP2 den heterodimeren RAB3GAP-Komplex, der bisher nur bekannt war für die Stimulation der Umwandlung der GTP-gebundenen aktiven Form zur GDP-gebundenen inaktiven Form der RAB GTPase RAB3. In Immunoblot-Analysen und mikroskopischen Darstellungen im Säugersystem konnte gezeigt werden, dass die Effekte auf die Proteostase über den autophagosomalen Abbauweg wirken. RAB3GAP1/2 wirken als positive Stimulatoren, wenn die Lipidierung von LC3-I und der autophagische Flux von LC3-II und p62/SQSTM1 betrachtet werden. Diese Effekte werden aber nicht über die RAB GTPase RAB3 vermittelt. Die Proteine FEZ1 und FEZ2 haben einen antagonistischen Effekt auf die Autophagie und wenn alle vier Komponenten RAB3GAP1, RAB3GAP2, FEZ1 und FEZ2 zusammen herunter- oder hochreguliert werden, heben sich diese Effekte auf. In Co-Immunopräzipitationen und proteomischen Analysen konnte keine direkte Interaktion zwischen dem RAB3GAP-Komplex und FEZ1/2 oder zu anderen Autophagie-Genen nachgewiesen werden.rnHier konnte der RAB3GAP-Komplex funktionell mit Proteostase und Autophagie in C. elegans und Säugerzellen assoziiert werden. Dieser Komplex zeigt Einflüsse auf die autophagosomale Biogenese indem sie die Proteostase und die Bildung von (prä)autophagosomalen Strukturen in C. elegans und die Lipidierung von LC3 und damit den autophagischen Flux der Autophagiesubstrate LC3-II und p62/SQSTM1 in Säugerzellen beeinflusst. Darüber hinaus wirkt RAB3GAP der komplexen Autophagie-Unterdrückung durch FEZ1 und FEZ2 entgegen. Somit konnte gezeigt werden, dass RAB3GAP als neuartiger Faktor auf die autophagosomale Biogenese und somit auf die Proteostase wirkt.rn