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.

Theoretical investigation of the interaction of a polymer film with a nanoparticle

The fundamental aim in our investigation of the interaction of a polymer film with a nanoparticle is the extraction of information on the dynamics of the liquid using a single tracking particle. In this work two theoretical methods were used: one passive, where the motion of the particle measures the dynamics of the liquid, one active, where perturbations in the system are introduced through the particle. In the first part of this investigation a thin polymeric film on a substrate is studied using molecular dynamics simulations. The polymer is modeled via a 'bead spring' model. The particle is spheric and non structured and is able to interact with the monomers via a Lennard Jones potential. The system is micro-canonical and simulations were performed for average temperatures between the glass transition temperature of the film and its dewetting temperature. It is shown that the stability of the nanoparticle on the polymer film in the absence of gravity depends strongly on the form of the chosen interaction potential between nanoparticle and polymer. The relative position of the tracking particle to the liquid vapor interface of the polymer film shows the glass transition of the latter. The velocity correlation function and the mean square displacement of the particle has shown that it is caged when the temperature is close to the glass transition temperature. The analysis of the dynamics at long times shows the coupling of the nanoparticle to the center of mass of the polymer chains. The use of the Stokes-Einstein formula, which relates the diffusion coefficient to the viscosity, permits to use the nanoparticle as a probe for the determination of the bulk viscosity of the melt, the so called 'microrheology'. It is shown that for low frequencies the result obtained using microrheology coincides with the results of the Rouse model applied to the polymer dynamics. In the second part of this investigation the equations of Linear Hydrodynamics are solved for a nanoparticle oscillating above the film. It is shown that compressible liquids have mechanical response to external perturbations induced with the nanoparticle. These solutions show strong velocity and pressure profiles of the liquid near the interface, as well as a mechanical response of the liquid-vapor interface. The results obtained with this calculations can be employed for the interpretation of experimental results of non contact AFM microscopy

Enzyme tRNA interaction and (t)RNA conformation probed via environmentally sensitive cyanine dyes

Nukleosidmodifikationen beeinflussen Dynamik und Konformation von RNArnund sind epigenetisch wirksam. Wenig verstanden sind konformationelle Dynamik und enzymatische Erkennung von tRNA, sowie der Einfluss des mutmaßlichen kovalenten Inhibitors 5-Fluorouridine (5FU) auf Y Synthasen, die Pseudouridin (Y) erzeugen. Frühere Arbeiten nutzten mit den Fluorophoren Cy3 und Cy5rnmarkierte tRNA, um diese Fragen zu adressieren.rnDie vorliegende Arbeit weitet Cy3-Cy5-Markierung auf Hefe tRNArnPhernaus undrnnutzt Thermophorese und fortschrittliche Fluoreszenzspektroskopie. In der Thermophorese zeigte sich eine hohe Toleranz gegenüber Fluoreszenzmarkierung beirngleichzeitiger Erhöhung der Cy5 Fluoreszenz durch Enzymbindung. Zudem konnte die Konformation verschiedener Mutanten human mitochondrialer tRNArnLysrnund die Bindung von SAM durch SAM-I Riboswitch RNA untersucht werden.rnUm etwaige Unterschiede in der Interaktion von Y55 Synthase TruB mit Cy5-gelabelter U55- bzw. 5FU55-tRNA aufzudecken, wurde eine Kombination ausrnThermophorese, zeit- und polarisationsaufgelöster Fluoreszenzspektroskopie undrn’gel shift’ Experimenten genutzt. Alle Ergebnisse zeigten übereinstimmend einernreversible Bindung ähnlicher Affinität für beide tRNAs und widersprechen somit einer kovalenten Inhibition durch 5FU. Folgerichtig wurde der SDS-stabilernKomplex von TruB mit 5FU-tRNA neu evaluiert, da er bisher als kovalent interpretiert wurde. Es erfolgte eine schnelle Komplexbildung in hoher Ausbeute auchrnfür schlechte Substrate, außerdem ließ sich die Komplexausbeute nicht durch andere Reaktionsbedingungen beeinflussen. Somit kann der SDS stabile Komplexrnnur den ersten, nicht-kovalenten Kontakt von Enzym und 5FU55-tRNA darstellen und repräsentiert kein kovalentes Addukt späterer Katalyse.

First contact imaging of nanoparticular siRNA – From synthesis to application of a prodye concept

Delivery of therapeutic nucleic acid based drugs is still very demanding and difficult to manage and monitor. For this reason, a precise method for the monitoring of RNAi pathways is necessary. This thesis explores a new approach for sensing of potentially therapeutic nucleic acids, using the interaction of so called prodyes with intracellular enzymes in a prodrug manner. To realize this concept, some non-fluorescent, fluorescein based asymmetric dyes were synthesized and their spectroscopic characteristics were studied. Azide-alkyne Click chemistry was applied for conjugation purposes, using a new protocol at weak acidic pH to get intact prodye constructs. Both, an electrophoretic mobility shift assay with polyacrylamide gels and in-cuvette experiments showed remarkable OFF-to-ON behavior of these new siRNA constructs under physiological conditions. After salt-free purification, subsequent hybridization to double-stranded ribonucleic acids and nanoformulation to lipoplexes, the prodye conjugated siRNA was examined in cellular uptake studies for First Contact Imaging. The investigated siRNA-prodye conjugates showed strong sensitivity to esterases, being hydrolyzed at the biolabile function and developing a strong fluorescence which was verified in bulk. As an optimization, a new profluorescent molecule system was designed and synthesized, which has a carbonate as biolabile 6’ protecting group and a highly water soluble 3’ clickable linker. This new non-fluorescent but colored prodye showed 12 - 320 times increased fluorescence intensities between OFF- and ON- states, depending to the deprotection method. This is the first reported molecule model of an asymmetric profluorescent fluorescein, having the very favorable 3’ & 6’ functions.