Condensazione di Bose-Einstein in trappole ottiche

Questo lavoro di tesi si occupa dello studio del fenomeno di condensazione di Bose-Einstein sia da un punto di vista teorico che, in maniera più accennata, da quello pratico-sperimentale; risulta pertanto strutturato in due parti. La prima è incentrata sull'analisi prettamente teorico-matematica dell'argomento, e si apre con l'introduzione dell'opportuno apparato formale atto alla trattazione della statistica quantistica; a tal proposito vengono definiti gli operatori di densità. Quindi viene affrontato il problema dell'indistinguibilità degli enti quantistici e del conseguente carattere di simmetria delle funzioni d'onda, individuando così la differenza tra particelle fermioniche e bosoniche. Di queste ultime vengono largamente studiate la statistica cui essere rispondono e le loro principali caratteristiche termodinamiche. Infine, viene analizzato il caso specifico del gas ideale di Bose, trattato nei limiti del continuo e termodinamico; è nel corso di questa trattazione che emerge il fenomeno di transizione chiamato condensazione di Bose-Einstein, di cui vengono ampiamente studiate le proprietà. La seconda parte, invece, è volta all'analisi delle tecniche sperimentali utilizzate per la realizzazione della condensazione, in particolare le trappole ottiche di dipolo; dopo averne studiato le caratteristiche, vengono illustrate alcune tecniche di raffreddamento di atomi intrappolati. Il lavoro si conclude con la trattazione delle principali tecniche diagnostiche e di riconoscimento del condensato.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.

Dynamics of dissipative Bose-Einstein condensation

We resolve the real-time dynamics of a purely dissipative s=1/2 quantum spin or, equivalently, hard-core boson model on a hypercubic d-dimensional lattice. The considered quantum dissipative process drives the system to a totally symmetric macroscopic superposition in each of the S3 sectors. Different characteristic time scales are identified for the dynamics and we determine their finite-size scaling. We introduce the concept of cumulative entanglement distribution to quantify multiparticle entanglement and show that the considered protocol serves as an efficient method to prepare a macroscopically entangled Bose-Einstein condensate.

Albert Einstein [Illustration] : nach einer Original-Radierung

Hermann Struck

Einstein

-tz.

Porträtbüste Professor Albert Einstein [Illustration]

Moshe Ziffer

Evaluation of elevator shafts as a pathway for fungal spores and particles to enter a hospital housing immuno-compromised patients

Background. It is estimated that hospitals spend between 28 and 33 billion dollars per year as a result of hospital-acquired infections. (Scott, 2009) The costs continue to rise despite the guidance and controls provided by hospital infection control staff to reduce patient exposures to fungal spores and other infectious agents. With all processes and controls in place, the vented elevator shaft represents an unprotected opening from the top of the building to the lower floors. The hypothesis for this prospective study is that there is a positive correlation between the number of Penicillium/Aspergillus-like spores, Cladosporium, ascospores, basidiospores in spores/m3 as individual spore categories found in the hoistway vent of an elevator shaft and the levels of the same spores, sampled near-simultaneously in the outdoor intake of the elevator shaft. Specific aims of this study include determining if external Penicillium/Aspergillus-like spores are entering the healthcare facility via the elevator shaft and hoistway vents. Additional aims include determining levels of Penicillium/Aspergillus-like spores outdoors, in the elevator shafts, and indoors in areas possibly affected by elevator shaft air; and, finally, to evaluate whether any effect is observed due to the installation of a hoistway vent damper, installed serendipitously during this study. ^ Methods. Between April 2010 and September 2010, a total of 3,521 air samples were collected, including 363 spore trap samples analyzed microscopically for seven spore types, and polymerase chain reaction analyses on 254 air samples. 2178 particle count measurements, 363 temperature readings and 363 relative humidity readings were also obtained from 7 different locations potentially related to the path of air travel inside and near a centrally-located and representative elevator shaft. ^ Results. Mean Penicillium/Aspergillus-like spore values were higher outside the building (530 spores/m3 of air) than inside the hoistway (22.8 spores/m3) during the six month study. Mean values inside the hospital were lower than outside throughout the study, ranging from 15 to 73 spores/m3 of air. Mean Penicillium/Aspergillus-like spore counts inside the hoistway decreased from 40.1 spores/m3 of air to 9 spores/m3 of air following the installation of a back draft damper between the outside air and the elevator shaft. Comparison of samples collected outside the building and inside the hoistway vent prior to installing the damper indicated a strong positive correlation (Spearman's Rho=0.8008, p=0.0001). The similar comparison following the damper installation indicated a moderate non-significant inverse correlation (Spearman's rho = −0.2795, p=0.1347). ^ Conclusion. Elevator shafts are one pathway for mold spores to enter a healthcare facility. A significant correlation was detected between spores and particle counts inside the hoistway and outside prior to changes in the ventilation system. The insertion of the back draft damper appeared to lower the spore counts inside the hoistway and inside the building. The mold spore counts in air outside the study building were higher in the period following the damper installation while the levels inside the hoistway and hospital decreased. Cladosporium and Penicillium/Aspergillus -like spores provided a method for evaluating indoor air quality as a natural tracer from outside the building to inside the building. Ascospores and basidiospores were not a valuable tracer due to low levels of detection during this study. ^ Installation of a back draft damper provides additional protection for the indoor environment of a hospital or healthcare facility, including in particular patients who may be immunocompromised. Current design standards and references do not require the installation of a back draft damper, but evaluation of adding language to relevant building codes should be considered. The data indicate a reduction in levels of Penicillium/Aspergillus -like spores, particle counts and a reduction in relative humidity inside of the elevator shaft after damper installation.^