Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Diffusion of laser polarized gases in MRI

The use of Magnetic Resonance Imaging (MRI) as a diagnostic tool is increasingly employing functional contrast agents to study or contrast entire mechanisms. Contrast agents in MRI can be classified in two categories. One type of contrast agents alters the NMR signal of the protons in its surrounding, e.g. lowers the T1 relaxation time. The other type enhances the Nuclear Magnetic Resonance (NMR) signal of specific nuclei. For hyperpolarized gases the NMR signal is improved up to several orders of magnitude. However, gases have a high diffusivity which strongly influences the NMR signal strength, hence the resolution and appearance of the images. The most interesting question in spatially resolved experiments is of course the achievable resolution and contrast by controlling the diffusivity of the gas. The influence of such diffusive processes scales with the diffusion coefficient, the strength of the magnetic field gradients and the timings used in the experiment. Diffusion may not only limit the MRI resolution, but also distort the line shape of MR images for samples, which contain boundaries or diffusion barriers within the sampled space. In addition, due to the large polarization in gaseous 3He and 129Xe, spin diffusion (different from particle diffusion) could play a role in MRI experiments. It is demonstrated that for low temperatures some corrections to the NMR measured diffusion coefficient have to be done, which depend on quantum exchange effects for indistinguishable particles. Physically, if these effects can not change the spin current, they can do it indirectly by modifying the velocity distribution of the different spin states separately, so that the subsequent collisions between atoms and therefore the diffusion coefficient can eventually be affected. A detailed study of the hyperpolarized gas diffusion coefficient is presented, demonstrating the absence of spin diffusion (different from particle diffusion) influence in MRI at clinical conditions. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. The experimental measured diffusion agrees with theoretical simulations. Therefore, the molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this allows for images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

Effizientes Vierwellenmischen durch Ausnutzen von Resonanzen in Quecksilber

In dieser Arbeit wird eine kohärente, kontinuierliche Strahlungsquelle im vakuum-ultravioletten (VUV) Spektrum vorgestellt. Sie basiert auf einem Vierwellenmischprozess in Quecksilberdampf mit Fundamentalstrahlen bei 253,7 nm, 407,9 nm und 545,5 nm Wellenlänge. Diese fundamentalen Strahlen werden durch frequenzverdoppelte bzw. frequenzvervierfachte Festkörperlasersysteme bereit gestellt. Durch das Ausnutzen der 6^1S-7^1S Zweiphotonenresonanz und zusätzlich der 6^1S-6^3P Einphotonenresonanz kann der Vierwellenmischprozess deutlich effizienter betrieben werden als zuvor. Eine nahe Einphotonenresonanz verringert die optimale Phasenanpassungstemperatur des Vierwellenmischprozesses, wodurch Druck- und Stoßverbreiterungen des Quecksilbers verkleinert und damit der nichtlineare Prozess effizienter wird. So können Leistungen bis zu 0,3 nW bei 121,56 nm, dem 1S-2P Lyman-alpha Übergang von Wasserstoff, erzeugt werden. Diese Lyman-alpha Quelle soll für die zukünftige Laserkühlung von Antiwasserstoff genutzt werden. rnrnNeben der Generierung von Strahlung bei Lyman-alpha kann, durch Veränderung der dritten Fundamentalwellenlänge, auch Strahlung in der Nähe zu einer Einphotonresonanz im VUV bei dem 6^1S-12^1P Übergang in Quecksilber durch Vierwellenmischen erzeugt werden. Durch diese weitere Einphotonresonanz kann die nichtlineare Suszeptibilität, verantwortlich für das Vierwellenmischen, stark vergrößert werden, ohne Einfluss auf die Phasenanpassung zu haben. Damit lässt sich der Mischprozess um drei Größenordnungen effizienter gestalten und Leistungen von 6 µW im VUV konnten realisiert werden. Dies entspricht einer Leistungsteigerung um einen Faktor 30 im Vergleich zu früheren Quellen. rnrnDarüberhinaus konnte die Zweiphotonenresonanz in Quecksilber ausführlich untersucht werden. Man erhält bei kleinen Rabifrequenzen der Fundamentalstrahlen eine geschwindigkeitsselektive Doppelresonanz, die den gleichen Ursprung wie Dunkelresonanzen in Lambda-Systemen hat. Bei hohen Rabifrequenzen kann die Anregung in das Zweiphotonenniveau so stark werden, dass auf dem 7^1S-6^1P Übergang ein Laserprozess initiiert wird. Dieser Prozess wurde hier zum ersten Mal mit kontinuierlichen Fundamentallasern nachgewiesen. Es wird gezeigt, dass der zusätzliche Laserprozess das Vierwellenmischen nicht beeinträchtigt.

The development and deployment of FOTOS: a fast observation of trace organics system

Flüchtige organische Bestandteile (engl.: VOC) sind in der Atmosphäre in Spuren vorhanden, spielen aber trotzdem eine wichtige Rolle in der Luftchemie: sie beeinflussen das Ozon der Troposphäre, städtischen Smog, Oxidationskapazität und haben direkte und indirekte Auswirkungen auf die globale Klimaveränderung. Eine wichtige Klasse der VOC sind die Nicht-Methan-Kohlenwasserstoffe (engl.: NMHC), die überwiegend von anthropogenen Quellen kommen. Aus diesem Grund ist für Luftchemiker ein Messinstrument nötig, das die VOC, die NMHC eingeschlossen, mit einer höheren Zeitauflösung misst, besonders für Echtzeitmessungen an Bord eines Forschungsflugzeuges. Dafür wurde das System zur schnellen Beobachtung von organischen Spuren (engl.: FOTOS) entworfen, gebaut für den Einsatz in einem neuen Wissenschaftlichen Flugzeug, das in großen Höhen und über weite Strecken fliegt, genannt HALO. In der Folge wurde FOTOS in zwei Messkampagnen am Boden getestet. FOTOS wurde entworfen und gebaut mit einem speziell angefertigten, automatisierten, kryogenen Probensystem mit drei Fallen und einem angepassten, erworbenen schnellen GC-MS. Ziel dieses Aufbaus war es, die Vielseitigkeit zu vergrößern und das Störungspotential zu verringern, deshalb wurden keine chemischen Trocknungsmittel oder adsorbierenden Stoffe verwendet. FOTOS erreichte eine Probenfrequenz von 5.5 Minuten, während es mindestens 13 verschiedene C2- bis C5-NMHC maß. Die Drei-Sigma-Detektionsgrenze für n- und iso-Pentan wurde als 2.6 und 2.0 pptv ermittelt, in dieser Reihenfolge. Labortests bestätigten, dass FOTOS ein vielseitiges, robustes, hochautomatisiertes, präzises, genaues, empfindliches Instrument ist, geeignet für Echtzeitmessungen von VOC in Probenfrequenzen, die angemessen sind für ein Forschungsflugzeug wie HALO. Um die Leistung von FOTOS zu bestätigen, wurde vom 26. Januar bis 4. Februar 2010 ein Zwischenvergleich gemacht mit dem GC-FID-System am Meteorologischen Observatorium Hohenpeißenberg, einer WMO-GAW-globalen Station. Dreizehn verschiedene NMHC wurden innerhalb des Rahmens der GWA Data Quality Objectives (DQO) analysiert und verglichen. Mehr als 80% der Messungen von sechs C3- bis C5-NMHC erfüllten diese DQO. Diese erste Messkampagne im Feld hob die Robustheit und Messgenauigkeit von FOTOS hervor, zusätzlich zu dem Vorteil der höheren Probenfrequenz, sogar in einer Messung am Boden. Um die Möglichkeiten dieses Instrumentes im Feld zu zeigen, maß FOTOS ausgewählte leichte NMHC während einer Messkampagne im Borealen Waldgebiet, HUMPPA-COPEC 2010. Vom 12. Juli bis zum 12. August 2010 beteiligte sich eine internationale Gruppe von Instituten und Instrumenten an Messungen physikalischer und chemischer Größen der Gas- und Partikelphasen der Luft über dem Borealen Wald an der SMEAR II-Station nahe Hyyttiälä, Finnland. Es wurden mehrere Hauptpunkte von Interesse im Mischungsverhältnis der Alkane und im Isomerenverhätnis von Pentan identifiziert, insbesondere sehr unterschiedliche Perioden niedriger und hoher Variabilität, drei Rauchschwaden von Biomassen-Verbrennung von russischen Waldbränden und zwei Tage mit extrem sauberer Luft aus der Polarregion. Vergleiche der NMHC mit anderen anthropogenen Indikatoren zeigten mehrere Quellen anthropogener Einflüsse am Ort auf und erlaubten eine Unterscheidung zwischen lokalen und weiter entfernten Quellen. Auf einen minimalen natürlichen Beitrag zum 24h-Kreislauf von NOx wurde geschlussfolgert aus der Korrelation von NOx mit Alkanen. Altersschätzungen der Luftmassen durch das Isomerenverhältnis von Pentan wurden erschwert durch sich verändernde Verhältnisse der Quellen und durch Besonderheiten der Photochemie während des Sommers im hohen Norden. Diese Messungen zeigten den Wert des Messens leichter NMHC, selbst in abgelegenen Regionen, als einen zusätzlichen spezifischen Marker von anthropogenem Einfluss.

Test der Speziellen Relativitätstheorie mittels Laserspektroskopie an relativistischen 7 Li +-Ionen am ESR

Die Invarianz physikalischer Gesetze unter Lorentztransformationen ist eines der fundamentalen Postulate der modernen Physik und alle Theorien der grundlegenden Wechselwirkungen sind in kovarianter Form formuliert. Obwohl die Spezielle Relativitätstheorie (SRT) in einer Vielzahl von Experimenten mit hoher Genauigkeit überprüft und bestätigt wurde, sind aufgrund der weitreichenden Bedeutung dieses Postulats weitere verbesserte Tests von grundsätzlichem Interesse. Darüber hinaus weisen moderne Ansätze zur Vereinheitlichung der Gravitation mit den anderen Wechselwirkungen auf eine mögliche Verletzung der Lorentzinvarianz hin. In diesem Zusammenhang spielen Ives-Stilwell Experimente zum Test der Zeitdilatation in der SRT eine bedeutende Rolle. Dabei wird die hochauflösende Laserspektroskopie eingesetzt, um die Gültigkeit der relativistischen Dopplerformel – und damit des Zeitdilatationsfaktors γ – an relativistischen Teilchenstrahlen zu untersuchen. Im Rahmen dieser Arbeit wurde ein Ives-Stilwell Experiment an 7Li+-Ionen, die bei einer Geschwindigkeit von 34 % der Lichtgeschwindigkeit im Experimentierspeicherring (ESR) des GSI Helmholtzzentrums für Schwerionenforschung gespeichert waren, durchgeführt. Unter Verwendung des 1s2s3S1→ 1s2p3P2-Übergangs wurde sowohl Λ-Spektroskopie als auch Sättigungsspektroskopie betrieben. Durch die computergestützte Analyse des Fluoreszenznachweises und unter Verwendung optimierter Kantenfilter für den Nachweis konnte das Signal zu Rauschverhältnis entscheidend verbessert und unter Einsatz eines zusätzlichen Pumplasers erstmals ein Sättigungssignal beobachtet werden. Die Frequenzstabilität der beiden verwendeten Lasersysteme wurde mit Hilfe eines Frequenzkamms spezifiziert, um eine möglichst hohe Genauigkeit zu erreichen. Die aus den Strahlzeiten gewonnen Daten wurden im Rahmen der Robertson-Mansouri-Sexl-Testtheorie (RMS) und der Standard Model Extension (SME) interpretiert und entsprechende Obergrenzen für die relevanten Testparameter der jeweiligen Theorie bestimmt. Die Obergrenze für den Testparameter α der RMS-Theorie konnte gegenüber den früheren Messungen bei 6,4 % der Lichtgeschwindigkeit am Testspeicherring (TSR) des Max-Planck-Instituts für Kernphysik in Heidelberg um einen Faktor 4 verbessert werden.

Total OH reactivity measurements at the biosphere-atmosphere interface

The biosphere emits copiously volatile organic compounds (VOCs) into the atmosphere, which are removed again depending on the oxidative capacity of the atmosphere and physical processes such as mixing, transport and deposition. Biogenic VOCs react with the primary oxidant of the atmosphere, the hydroxyl radical (OH), and potentially lead to the formation tropospheric ozone and aerosol, which impact regional climate and air quality. The rate of OH decay in the atmosphere, the total OH reactivity is a function of the atmospheric, reactive compound's concentration and reaction velocity with OH. One way to measure the total OH reactivity, the total OH sink, is with the Comparative Reactivity Method - CRM. Basically, the reaction of OH with a reagent (here pyrrole) in clean air and in the presence of atmospheric, reactive molecules is compared. This thesis presents measurements of the total OH reactivity at the biosphere-atmosphere interface to analyze various influences and driving forces. For measurements in natural environment the instrument was automated and a direct, undisturbed sampling method developed. Additionally, an alternative detection system was tested and compared to the originally used detector (Proton Transfer Reaction-Mass Spectrometer, PTR-MS). The GC-PID (Gas Chromatographic Photo-Ionization Detector) was found as a smaller, less expensive, and robust alternative for total OH reactivity measurements. The HUMPPA-COPEC 2010 measurement campaign in the Finish forest was impacted by normal boreal forest emissions as well as prolonged heat and biomass burning emissions. The measurement of total OH reactivity was compared with a comprehensive set of monitored individual species ambient concentration levels. A significant discrepancy between those individually measured OH sinks and the total OH reactivity was observed, which was characterized in detail by the comparison of within and above the forest canopy detected OH reactivity. Direct impact of biogenic emissions on total OH reactivity was examined on Kleiner Feldberg, Germany, 2011. Trans-seasonal measurements of an enclosed Norway spruce branch were conducted via PTR-MS, for individual compound's emission rates, and CRM, for total OH reactivity emission fluxes. Especially during summertime, the individually monitored OH sink terms could not account for the measured total OH reactivity. A controlled oxidation experiment in a low NOx environment was conducted in the EUPHORE reaction chamber (CHEERS, Spain 2011). The concentration levels of the reactant isoprene and its major products were monitored and compared to total OH reactivity measurements as well as to the results of two models. The individually measured compounds could account for the total OH reactivity during this experiment as well as the traditional model-degradation scheme for isoprene (MCM 3.2). Due to previous observations of high OH levels in the isoprene-rich environment of the tropics, a novel isoprene mechanism was recently suggested. In this mechanism (MIME v4) additional OH is generated during isoprene oxidation, which could not be verified in the conditions of the CHEERS experiment.

Atmospheric and climate effects of biomass burning using different injection heights

Inspired by the need for a representation of the biomass burning emissions injection height in the ECHAM/MESSy Atmospheric Chemistry model (EMAC)

Monte Carlo simulations of nucleation of colloidal crystals

A crystal nucleus in a finite volume may exhibit phase coexistence with a surrounding fluid. The thermodynamic properties of the coexisting fluid (pressure and chemical potential) are enhanced relative to their coexistence values. This enhancement is uniquely related to the surface excess free energy. rnA model for weakly attractive soft colloidal particles is investigated, the so called Asakura-Oosawa model. In simulations, this model allows for the calculation of the pressure in the liquid using the virial formula directly. The phase coexistence pressure in the thermodynamic limit is obtained from the interface velocity method. We introduce a method by which the chemical potential in dense liquids can be measured. There is neither a need to locate the interface nor to compute the anisotropic interfacial tension to obtain nucleation barriers. Therefore, our analysis is appropriate for nuclei of arbitrary shape. Monte Carlo simulations over a wide range of nucleus volumes yield to nucleation barriers independent from the total system volume. The interfacial tension is determined via the ensemble-switch method, hence a detailed test of classical nucleation theory is possible. The anisotropy of the interfacial tension and the resulting non-spherical shape has only a minor effect on the barrier for the Asakura-Oosawa model.

The velocity dispersion profile of the globular cluster 47Tucanae

Gli ammassi globulari rappresentano i laboratori ideali nei quali studiare la dinamica di sistemi ad N-corpi ed i suoi effetti sull’evoluzione stellare. Infatti, gli ammassi globulari sono gli unici sistemi astrofisici che, entro il tempo scala dell’età dell’Universo, sperimentano quasi tutti i processi di dinamica stellare noti. Questo lavoro di tesi si inserisce in un progetto a lungo termine volto a fornire una dettagliata caratterizzazione delle proprietà dinamiche degli ammassi globulari galattici. In questa ricerca, strumenti di fondamentale importanza sono il profilo di dispersione di velocità del sistema e la sua curva di rotazione. Per determinare le componenti radiali di questi profili cinematici in ammassi globulari galattici è necessario misurare la velocità lungo la linea di vista di un ampio campione di stelle membre, a differenti distanze dal centro. Seguendo un approccio multi-strumentale, è possibile campionare l’intera estensione radiale dell’ammasso utilizzando spettrografi multi-oggetto ad alta risoluzione spettrale nelle regioni intermedie/esterne, e spettrografi IFU con ottiche adattive per le regioni centrali (pochi secondi d’arco dal centro). Questo lavoro di tesi è volto a determinare il profilo di dispersione di velocità dell’ammasso globulare 47 Tucanae, campionando un’estensione radiale compresa tra circa 20'' e 13' dal centro. Per questo scopo sono state misurate le velocità radiali di circa un migliaio di stelle nella direzione di 47 Tucanae, utilizzando spettri ad alta risoluzione ottenuti con lo spettrografo multi-oggetto FLAMES montato al Very Large Telescope dell’ESO. Le velocità radiali sono state misurate utilizzando la tecnica di cross-correlazione tra gli spettri osservati e appropriati spettri teorici, e sono state ottenute accuratezze inferiori a 0.5km/s. Il campione così ottenuto (complementare a quello raccolto con strumenti IFU nelle regioni centrali) è fondamentale per costruire il profilo di dispersione di velocità dell’ammasso e la sua eventuale curva di rotazione. Questi dati, combinati col profilo di densità dell’ammasso precedentemente determinato, permetteranno di vincolare opportunamente modelli teorici come quelli di King (1966) o di Wilson (1975), e di arrivare così alla prima solida determinazione dei parametri strutturali e dinamici (raggi di core e di metà massa, tempo di rilassamento, parametro collisionale, etc.) e della massa totale e distribuzione di massa del sistema.

Velocity recovery cycles of human muscle action potentials in chronic renal failure

To test the hypothesis that muscle fibers are depolarized in patients with chronic renal failure, by measuring velocity recovery cycles of muscle action potentials as indicators of muscle membrane potential.

Muscle membrane dysfunction in critical illness myopathy assessed by velocity recovery cycles

To test the hypothesis that muscle fibers are depolarized in patients with critical illness myopathy by measuring velocity recovery cycles (VRCs) of muscle action potentials.

Chest pulse-wave velocity: a novel approach to assess arterial stiffness

Pulse-wave velocity (PWV) is considered as the gold-standard method to assess arterial stiffness, an independent predictor of cardiovascular morbidity and mortality. Current available devices that measure PWV need to be operated by skilled medical staff, thus, reducing the potential use of PWV in the ambulatory setting. In this paper, we present a new technique allowing continuous, unsupervised measurements of pulse transit times (PTT) in central arteries by means of a chest sensor. This technique relies on measuring the propagation time of pressure pulses from their genesis in the left ventricle to their later arrival at the cutaneous vasculature on the sternum. Combined thoracic impedance cardiography and phonocardiography are used to detect the opening of the aortic valve, from which a pre-ejection period (PEP) value is estimated. Multichannel reflective photoplethysmography at the sternum is used to detect the distal pulse-arrival time (PAT). A PTT value is then calculated as PTT = PAT - PEP. After optimizing the parameters of the chest PTT calculation algorithm on a nine-subject cohort, a prospective validation study involving 31 normo- and hypertensive subjects was performed. 1/chest PTT correlated very well with the COMPLIOR carotid to femoral PWV (r = 0.88, p < 10 (-9)). Finally, an empirical method to map chest PTT values onto chest PWV values is explored.