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.

Detection of small buried objects: asymptotic factorization and MUSIC

In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an unbounded two–layered background medium. In possible applications, such as, e.g., humanitarian demining, the two layers would correspond to air and soil. Moving a set of electric devices parallel to the surface of ground to generate a time–harmonic field, the induced field is measured within the same devices. The goal is to retrieve information about buried scatterers from these data. In mathematical terms, we are concerned with the analysis and numerical solution of the inverse scattering problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two–layered background medium from near field measurements of time–harmonic electromagnetic waves. For this purpose, we first study the corresponding direct scattering problem in detail and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero. Then, we use this expansion to justify a noniterative MUSIC–type reconstruction method for the solution of the inverse scattering problem. We propose a numerical implementation of this reconstruction method and provide a series of numerical experiments.

Einfluss der Einzeldosisblisterverpackung von festen Oralia auf die Arzneimitteltherapiesicherheit, Information und Zufriedenheit stationär behandelter Patienten in einer prospektiven, multizentrischen Studie

Bei der vorliegenden Studie wurde die Machbarkeit und Qualität der Arzneimittelverteilung von oralen Arzneimitteln in Einzeldosisblisterverpackungen je abgeteilte Arzneiform (EVA) untersucht.rnDie Studie wurde als offene, vergleichende, prospektive und multizentrische Patientenstudie durchgeführt. Als Studienmedikation standen Diovan®, CoDiovan® und Amlodipin in der EVA-Verpackung zur Verfügung. Die Verteilfehlerrate in der EVA- und Kontroll-Gruppe stellte den primären Zielparameter dar. Das Patientenwissen, die Patientenzufriedenheit und die Praktikabilität des EVA-Systems, sowie die Zufriedenheit der Pflegekräfte wurden mithilfe von Fragebogen evaluiert. Insgesamt wurden 2070 gültige Tablettenvergaben bei 332 Patienten in sechs verschiedenen Krankenhäusern geprüft. Es wurde in der EVA-Gruppe ein Verteilungsfehler von 1,8% und in der Kontroll-Gruppe von 0,7% ermittelt. Bei den Patienten-Fragebogen konnten insgesamt 292 Fragebogen ausgewertet werden. Die Ergebnisse zeigten einen ungenügenden Informationsstand der Patienten über ihre aktuellen, oralen Arzneimittel. In den 80 ausgefüllten Pflegekräfte-Fragebogen gaben über 80% an, dass Fehler beim Richten durch das EVA-System besser erkannt werden können. rnZusammenfassend kann gesagt werden, dass die erhöhte Fehlerrate in der EVA-Gruppe im Vergleich zur Kontroll-Gruppe durch mehrere Störfaktoren bedingt wurde. Grundsätzlich konnte eine sehr positive Resonanz auf das EVA-System bei den Patienten und den Pflegekräften beobachtet werden. rn