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The need to reduce humankind reliance on fossil fuels by exploiting sustainably the planet renewable resources is a major driving force determining the focus of modern material research. For this reason great interest is nowadays focused on finding alternatives to fossil fuels derived products/materials. For the short term the most promising substitute is undoubtedly biomass, since it is the only renewable and sustainable alternative to fossil fuels as carbon source. As a consequence efforts, aimed at finding new synthetic approaches to convert biomass and its derivatives into carbon-based materials, are constantly increasing. In this regard, hydrothermal carbonisation (HTC) has shown to be an effective means of conversion of biomass-derived precursors into functional carbon materials. However the attempts to convert raw biomass, in particular lignocellulosic one, directly into such products have certainly been rarer. Unlocking the direct use of these raw materials as carbon precursors would definitely be beneficial in terms of HTC sustainability. For this reason, in this thesis the HTC of carbohydrate and protein-rich biomass was systematically investigated, in order to obtain more insights on the potentials of this thermochemical processing technique in relation to the production of functional carbon materials from crude biomass. First a detailed investigation on the HTC conversion mechanism of lignocellulosic biomass and its single components (i.e. cellulose, lignin) was developed based on a comparison with glucose HTC, which was adopted as a reference model. In the glucose case it was demonstrated that varying the HTC temperature allowed tuning the chemical structure of the synthesised carbon materials from a highly cross-linked furan-based structure (T = 180oC) to a carbon framework composed of polyaromatic arene-like domains. When cellulose or lignocellulosic biomass was used as carbon precursor, the furan rich structure could not be isolated at any of the investigated processing conditions. These evidences were indicative of a different HTC conversion mechanism for cellulose, involving reactions that are commonly observed during pyrolytic processes. The evolution of glucose-derived HTC carbon chemical structure upon pyrolysis was also investigated. These studies revealed that upon heat treatment (Investigated temperatures 350 – 900 oC) the furan-based structure was progressively converted into highly curved aromatic pre-graphenic domains. This thermal degradation process was observed to produce an increasingly more hydrophobic surface and considerable microporosity within the HTC carbon structure. In order to introduce porosity in the HTC carbons derived from lignocellulosic biomass, KOH chemical activation was investigated as an HTC post-synthesis functionalisation step. These studies demonstrated that HTC carbons are excellent precursors for the production of highly microporous activated carbons (ACs) and that the porosity development upon KOH chemical activation is dependent on the chemical structure of the HTC carbon, tuned by employing different HTC temperatures. Preliminary testing of the ACs for CO2 capture or high pressure CH4 storage yielded very promising results, since the measured uptakes of both adsorbates (i.e. CO2 and CH4) were comparable to top-performing and commercially available adsorbents, usually employed for these end-applications. The combined use of HTC and KOH chemical activation was also employed to produce highly microporous N-doped ACs from microalgae. The hydrothermal treatment of the microalgae substrate was observed to cause the depletion of the protein and carbohydrate fractions and the near complete loss (i.e. 90%) of the microalgae N-content, as liquid hydrolysis/degradation products. The obtained carbonaceous product showed a predominantly aliphatic character indicating the presence of alkyl chains presumably derived from the lipid fractions. Addition of glucose to the initial reaction mixture was found out to be extremely beneficial, because it allowed the fixation of a higher N amount, in the algae derived HTC carbons (i.e. 60%), and the attainment of higher product yields (50%). Both positive effects were attributed to Maillard type cascade reactions taking place between the monosaccharides and the microalgae derived liquid hydrolysis/degradation products, which were in this way recovered from the liquid phase. KOH chemical activation of the microalgae/glucose mixture derived HTC carbons produced highly microporous N-doped carbons. Although the activation process led to a major reduction of the N-content, the retained N-amount in the ACs was still considerable. These features render these materials ideal candidates for supercapacitors electrodes, since they provide extremely high surface areas, for the formation of electric double-layer, coupled to abundant heteroatom doping (i.e. N and O) necessary to obtain a pseudocapacitance contribution.
Structuring process models
(2012)
One can fairly adopt the ideas of Donald E. Knuth to conclude that process modeling is both a science and an art. Process modeling does have an aesthetic sense. Similar to composing an opera or writing a novel, process modeling is carried out by humans who undergo creative practices when engineering a process model. Therefore, the very same process can be modeled in a myriad number of ways. Once modeled, processes can be analyzed by employing scientific methods. Usually, process models are formalized as directed graphs, with nodes representing tasks and decisions, and directed arcs describing temporal constraints between the nodes. Common process definition languages, such as Business Process Model and Notation (BPMN) and Event-driven Process Chain (EPC) allow process analysts to define models with arbitrary complex topologies. The absence of structural constraints supports creativity and productivity, as there is no need to force ideas into a limited amount of available structural patterns. Nevertheless, it is often preferable that models follow certain structural rules. A well-known structural property of process models is (well-)structuredness. A process model is (well-)structured if and only if every node with multiple outgoing arcs (a split) has a corresponding node with multiple incoming arcs (a join), and vice versa, such that the set of nodes between the split and the join induces a single-entry-single-exit (SESE) region; otherwise the process model is unstructured. The motivations for well-structured process models are manifold: (i) Well-structured process models are easier to layout for visual representation as their formalizations are planar graphs. (ii) Well-structured process models are easier to comprehend by humans. (iii) Well-structured process models tend to have fewer errors than unstructured ones and it is less probable to introduce new errors when modifying a well-structured process model. (iv) Well-structured process models are better suited for analysis with many existing formal techniques applicable only for well-structured process models. (v) Well-structured process models are better suited for efficient execution and optimization, e.g., when discovering independent regions of a process model that can be executed concurrently. Consequently, there are process modeling languages that encourage well-structured modeling, e.g., Business Process Execution Language (BPEL) and ADEPT. However, the well-structured process modeling implies some limitations: (i) There exist processes that cannot be formalized as well-structured process models. (ii) There exist processes that when formalized as well-structured process models require a considerable duplication of modeling constructs. Rather than expecting well-structured modeling from start, we advocate for the absence of structural constraints when modeling. Afterwards, automated methods can suggest, upon request and whenever possible, alternative formalizations that are "better" structured, preferably well-structured. In this thesis, we study the problem of automatically transforming process models into equivalent well-structured models. The developed transformations are performed under a strong notion of behavioral equivalence which preserves concurrency. The findings are implemented in a tool, which is publicly available.
Structural dynamics of photoexcited nanolayered perovskites studied by ultrafast x-ray diffraction
(2012)
This publication-based thesis represents a contribution to the active research field of ultrafast structural dynamics in laser-excited nanostructures. The investigation of such dynamics is mandatory for the understanding of the various physical processes on microscopic scales in complex materials which have great potentials for advances in many technological applications. I theoretically and experimentally examine the coherent, incoherent and anharmonic lattice dynamics of epitaxial metal-insulator heterostructures on timescales ranging from femtoseconds up to nanoseconds. To infer information on the transient dynamics in the photoexcited crystal lattices experimental techniques using ultrashort optical and x-ray pulses are employed. The experimental setups include table-top sources as well as large-scale facilities such as synchrotron sources. At the core of my work lies the development of a linear-chain model to simulate and analyze the photoexcited atomic-scale dynamics. The calculated strain fields are then used to simulate the optical and x-ray response of the considered thin films and multilayers in order to relate the experimental signatures to particular structural processes. This way one obtains insight into the rich lattice dynamics exhibiting coherent transport of vibrational energy from local excitations via delocalized phonon modes of the samples. The complex deformations in tailored multilayers are identified to give rise to highly nonlinear x-ray diffraction responses due to transient interference effects. The understanding of such effects and the ability to precisely calculate those are exploited for the design of novel ultrafast x-ray optics. In particular, I present several Phonon Bragg Switch concepts to efficiently generate ultrashort x-ray pulses for time-resolved structural investigations. By extension of the numerical models to include incoherent phonon propagation and anharmonic lattice potentials I present a new view on the fundamental research topics of nanoscale thermal transport and anharmonic phonon-phonon interactions such as nonlinear sound propagation and phonon damping. The former issue is exemplified by the time-resolved heat conduction from thin SrRuO3 films into a SrTiO3 substrate which exhibits an unexpectedly slow heat conductivity. Furthermore, I discuss various experiments which can be well reproduced by the versatile numerical models and thus evidence strong lattice anharmonicities in the perovskite oxide SrTiO3. The thesis also presents several advances of experimental techniques such as time-resolved phonon spectroscopy with optical and x-ray photons as well as concepts for the implementation of x-ray diffraction setups at standard synchrotron beamlines with largely improved time-resolution for investigations of ultrafast structural processes. This work forms the basis for ongoing research topics in complex oxide materials including electronic correlations and phase transitions related to the elastic, magnetic and polarization degrees of freedom.
Mit der Liberalisierung des Strommarkts, den unsicheren Aussichten in der Klimapolitik und stark schwankenden Preisen bei Brennstoffen, Emissionsrechten und Kraftwerkskomponenten hat bei Kraftwerksinvestitionen das Risikomanagement an Bedeutung gewonnen. Dies äußert sich im vermehrten Einsatz probabilistischer Verfahren. Insbesondere bei regulativen Risiken liefert der klassische, häufigkeitsbasierte Wahrscheinlichkeitsbegriff aber keine Handhabe zur Risikoquantifizierung. In dieser Arbeit werden Kraftwerksinvestitionen und -portfolien in Deutschland mit Methoden des Bayes'schen Risikomanagements bewertet. Die Bayes'sche Denkschule begreift Wahrscheinlichkeit als persönliches Maß für Unsicherheit. Wahrscheinlichkeiten können auch ohne statistische Datenanalyse allein mit Expertenbefragungen gewonnen werden. Das Zusammenwirken unsicherer Werttreiber wurde mit einem probabilistischen DCF-Modell (Discounted Cash Flow-Modell) spezifiziert und in ein Einflussdiagramm mit etwa 1200 Objekten umgesetzt. Da der Überwälzungsgrad von Brennstoff- und CO2-Kosten und damit die Höhe der von den Kraftwerken erwirtschafteten Deckungsbeiträge im Wettbewerb bestimmt werden, reicht eine einzelwirtschaftliche Betrachtung der Kraftwerke nicht aus. Strompreise und Auslastungen werden mit Heuristiken anhand der individuellen Position der Kraftwerke in der Merit Order bestimmt, d.h. anhand der nach kurzfristigen Grenzkosten gestaffelten Einsatzreihenfolge. Dazu wurden 113 thermische Großkraftwerke aus Deutschland in einer Merit Order vereinigt. Das Modell liefert Wahrscheinlichkeitsverteilungen für zentrale Größen wie Kapitalwerte von Bestandsportfolien sowie Stromgestehungskosten und Kapitalwerte von Einzelinvestitionen (Steinkohle- und Braunkohlekraftwerke mit und ohne CO2-Abscheidung sowie GuD-Kraftwerke). Der Wert der Bestandsportfolien von RWE, E.ON, EnBW und Vattenfall wird primär durch die Beiträge der Braunkohle- und Atomkraftwerke bestimmt. Erstaunlicherweise schlägt sich der Emissionshandel nicht in Verlusten nieder. Dies liegt einerseits an den Zusatzgewinnen der Atomkraftwerke, andererseits an den bis 2012 gratis zugeteilten Emissionsrechten, welche hohe Windfall-Profite generieren. Dadurch erweist sich der Emissionshandel in seiner konkreten Ausgestaltung insgesamt als gewinnbringendes Geschäft. Über die Restlaufzeit der Bestandskraftwerke resultiert ab 2008 aus der Einführung des Emissionshandels ein Barwertvorteil von insgesamt 8,6 Mrd. €. In ähnlicher Dimension liegen die Barwertvorteile aus der 2009 von der Bundesregierung in Aussicht gestellten Laufzeitverlängerung für Atomkraftwerke. Bei einer achtjährigen Laufzeitverlängerung ergäben sich je nach CO2-Preisniveau Barwertvorteile von 8 bis 15 Mrd. €. Mit höheren CO2-Preisen und Laufzeitverlängerungen von bis zu 28 Jahren würden 25 Mrd. € oder mehr zusätzlich anfallen. Langfristig erscheint fraglich, ob unter dem gegenwärtigen Marktdesign noch Anreize für Investitionen in fossile Kraftwerke gegeben sind. Zu Beginn der NAP 2-Periode noch rentable Investitionen in Braunkohle- und GuD-Kraftwerke werden mit der auslaufenden Gratiszuteilung von Emissionsrechten zunehmend unrentabler. Die Rentabilität wird durch Strommarkteffekte der erneuerbaren Energien und ausscheidender alter Gas- und Ölkraftwerke stetig weiter untergraben. Steinkohlekraftwerke erweisen sich selbst mit anfänglicher Gratiszuteilung als riskante Investition. Die festgestellten Anreizprobleme für Neuinvestitionen sollten jedoch nicht dem Emissionshandel zugeschrieben werden, sondern resultieren aus den an Grenzkosten orientierten Strompreisen. Das Anreizproblem ist allerdings bei moderaten CO2-Preisen am größten. Es gilt auch für Kraftwerke mit CO2-Abscheidung: Obwohl die erwarteten Vermeidungskosten für CCS-Kraftwerke gegenüber konventionellen Kohlekraftwerken im Jahr 2025 auf 25 €/t CO2 (Braunkohle) bzw. 38,5 €/t CO2 (Steinkohle) geschätzt werden, wird ihr Bau erst ab CO2-Preisen von 50 bzw. 77 €/t CO2 rentabel. Ob und welche Kraftwerksinvestitionen sich langfristig rechnen, wird letztlich aber politisch entschieden und ist selbst unter stark idealisierten Bedingungen kaum vorhersagbar.
In the course of this thesis gold nanoparticle/polyelectrolyte multilayer structures were prepared, characterized, and investigated according to their static and ultrafast optical properties. Using the dip-coating or spin-coating layer-by-layer deposition method, gold-nanoparticle layers were embedded in a polyelectrolyte environment with high structural perfection. Typical structures exhibit four repetition units, each consisting of one gold-particle layer and ten double layers of polyelectrolyte (cationic+anionic polyelectrolyte). The structures were characterized by X-ray reflectivity measurements, which reveal Bragg peaks up to the seventh order, evidencing the high stratication of the particle layers. In the same measurements pronounced Kiessig fringes were observed, which indicate a low global roughness of the samples. Atomic force microscopy (AFM) images veried this low roughness, which results from the high smoothing capabilities of polyelectrolyte layers. This smoothing effect facilitates the fabrication of stratified nanoparticle/polyelectrolyte multilayer structures, which were nicely illustrated in a transmission electron microscopy image. The samples' optical properties were investigated by static spectroscopic measurements in the visible and UV range. The measurements revealed a frequency shift of the reflectance and of the plasmon absorption band, depending on the thickness of the polyelectrolyte layers that cover a nanoparticle layer. When the covering layer becomes thicker than the particle interaction range, the absorption spectrum becomes independent of the polymer thickness. However, the reflectance spectrum continues shifting to lower frequencies (even for large thicknesses). The range of plasmon interaction was determined to be in the order of the particle diameter for 10 nm, 20 nm, and 150 nm particles. The transient broadband complex dielectric function of a multilayer structure was determined experimentally by ultrafast pump-probe spectroscopy. This was achieved by simultaneous measurements of the changes in the reflectance and transmittance of the excited sample over a broad spectral range. The changes in the real and imaginary parts of the dielectric function were directly deduced from the measured data by using a recursive formalism based on the Fresnel equations. This method can be applied to a broad range of nanoparticle systems where experimental data on the transient dielectric response are rare. This complete experimental approach serves as a test ground for modeling the dielectric function of a nanoparticle compound structure upon laser excitation.
This thesis is focussed on the electronic properties of the new material class named topological insulators. Spin and angle resolved photoelectron spectroscopy have been applied to reveal several unique properties of the surface state of these materials. The first part of this thesis introduces the methodical background of these quite established experimental techniques.
In the following chapter, the theoretical concept of topological insulators is introduced. Starting from the prominent example of the quantum Hall effect, the application of topological invariants to classify material systems is illuminated. It is explained how, in presence of time reversal symmetry, which is broken in the quantum Hall phase, strong spin orbit coupling can drive a system into a topologically non trivial phase. The prediction of the spin quantum Hall effect in two dimensional insulators an the generalization to the three dimensional case of topological insulators is reviewed together with the first experimental realization of a three dimensional topological insulator in the Bi1-xSbx alloys given in the literature.
The experimental part starts with the introduction of the Bi2X3 (X=Se, Te) family of materials. Recent theoretical predictions and experimental findings on the bulk and surface electronic structure of these materials are introduced in close discussion to our own experimental results. Furthermore, it is revealed, that the topological surface state of Bi2Te3 shares its orbital symmetry with the bulk valence band and the observation of a temperature induced shift of the chemical potential is to a high probability unmasked as a doping effect due to residual gas adsorption.
The surface state of Bi2Te3 is found to be highly spin polarized with a polarization value of about 70% in a macroscopic area, while in Bi2Se3 the polarization appears reduced, not exceeding 50%. We, however, argue that the polarization is most likely only extrinsically limited in terms of the finite angular resolution and the lacking detectability of the out of plane component of the electron spin. A further argument is based on the reduced surface quality of the single crystals after cleavage and, for Bi2Se3 a sensitivity of the electronic structure to photon exposure.
We probe the robustness of the topological surface state in Bi2X3 against surface impurities in Chapter 5. This robustness is provided through the protection by the time reversal symmetry. Silver, deposited on the (111) surface of Bi2Se3 leads to a strong electron doping but the surface state is observed up to a deposited Ag mass equivalent to one atomic monolayer. The opposite sign of doping, i.e., hole-like, is observed by exposing oxygen to Bi2Te3. But while the n-type shift of Ag on Bi2Se3 appears to be more or less rigid, O2 is lifting the Dirac point of the topological surface state in Bi2Te3 out of the valence band minimum at $\Gamma$. After increasing the oxygen dose further, it is possible to shift the Dirac point to the Fermi level, while the valence band stays well beyond. The effect is found reversible, by warming up the samples which is interpreted in terms of physisorption of O2.
For magnetic impurities, i.e., Fe, we find a similar behavior as for the case of Ag in both Bi2Se3 and Bi2Te3. However, in that case the robustness is unexpected, since magnetic impurities are capable to break time reversal symmetry which should introduce a gap in the surface state at the Dirac point which in turn removes the protection. We argue, that the fact that the surface state shows no gap must be attributed to a missing magnetization of the Fe overlayer. In Bi2Te3 we are able to observe the surface state for deposited iron mass equivalents in the monolayer regime. Furthermore, we gain control over the sign of doping through the sample temperature during deposition.
Chapter6 is devoted to the lifetime broadening of the photoemission signal from the topological surface states of Bi2Se3 and Bi2Te3. It is revealed that the hexagonal warping of the surface state in Bi2Te3 introduces an anisotropy for electrons traveling along the two distinct high symmetry directions of the surface Brillouin zone, i.e., $\Gamma$K and $\Gamma$M. We show that the phonon coupling strength to the surface electrons in Bi2Te3 is in nice agreement with the theoretical prediction but, nevertheless, higher than one may expect. We argue that the electron-phonon coupling is one of the main contributions to the decay of photoholes but the relatively small size of the Fermi surface limits the number of phonon modes that may scatter off electrons. This effect is manifested in the energy dependence of the imaginary part of the electron self energy of the surface state which shows a decay to higher binding energies in contrast to the monotonic increase proportional to E$^2$ in the Fermi liquid theory due to electron-electron interaction.
Furthermore, the effect of the surface impurities of Chapter 5 on the quasiparticle life- times is investigated. We find that Fe impurities have a much stronger influence on the lifetimes as compared to Ag. Moreover, we find that the influence is stronger independently of the sign of the doping. We argue that this observation suggests a minor contribution of the warping on increased scattering rates in contrast to current belief. This is additionally confirmed by the observation that the scattering rates increase further with increasing silver amount while the doping stays constant and by the fact that clean Bi2Se3 and Bi2Te3 show very similar scattering rates regardless of the much stronger warping in Bi2Te3.
In the last chapter we report on a strong circular dichroism in the angle distribution of the photoemission signal of the surface state of Bi2Te3. We show that the color pattern obtained by calculating the difference between photoemission intensities measured with opposite photon helicity reflects the pattern expected for the spin polarization. However, we find a strong influence on strength and even sign of the effect when varying the photon energy. The sign change is qualitatively confirmed by means of one-step photoemission calculations conducted by our collaborators from the LMU München, while the calculated spin polarization is found to be independent of the excitation energy. Experiment and theory together unambiguously uncover the dichroism in these systems as a final state effect and the question in the title of the chapter has to be negated: Circular dichroism in the angle distribution is not a new spin sensitive technique.
Soil conditions under vegetation cover and their spatial and temporal variations from point to catchment scale are crucial for understanding hydrological processes within the vadose zone, for managing irrigation and consequently maximizing yield by precision farming. Soil moisture and soil roughness are the key parameters that characterize the soil status. In order to monitor their spatial and temporal variability on large scales, remote sensing techniques are required. Therefore the determination of soil parameters under vegetation cover was approached in this thesis by means of (multi-angular) polarimetric SAR acquisitions at a longer wavelength (L-band, lambda=23cm). In this thesis, the penetration capabilities of L-band are combined with newly developed (multi-angular) polarimetric decomposition techniques to separate the different scattering contributions, which are occurring in vegetation and on ground. Subsequently the ground components are inverted to estimate the soil characteristics. The novel (multi-angular) polarimetric decomposition techniques for soil parameter retrieval are physically-based, computationally inexpensive and can be solved analytically without any a priori knowledge. Therefore they can be applied without test site calibration directly to agricultural areas. The developed algorithms are validated with fully polarimetric SAR data acquired by the airborne E-SAR sensor of the German Aerospace Center (DLR) for three different study areas in Germany. The achieved results reveal inversion rates up to 99% for the soil moisture and soil roughness retrieval in agricultural areas. However, in forested areas the inversion rate drops significantly for most of the algorithms, because the inversion in forests is invalid for the applied scattering models at L-band. The validation against simultaneously acquired field measurements indicates an estimation accuracy (root mean square error) of 5-10vol.% for the soil moisture (range of in situ values: 1-46vol.%) and of 0.37-0.45cm for the soil roughness (range of in situ values: 0.5-4.0cm) within the catchment. Hence, a continuous monitoring of soil parameters with the obtained precision, excluding frozen and snow covered conditions, is possible. Especially future, fully polarimetric, space-borne, long wavelength SAR missions can profit distinctively from the developed polarimetric decomposition techniques for separation of ground and volume contributions as well as for soil parameter retrieval on large spatial scales.
Education in knowledge society is challenged with a lot of problems in particular the interaction between the teacher and learner in social networking software as a key factor affects the learners’ learning and satisfaction (Prammanee, 2005) where “to teach is to communicate, to communicate is to interact, to interact is to learn” (Hefzallah, 2004, p. 48). Analyzing the relation between teacher-learner interaction from a side and learning outcome and learners’ satisfaction from the other side, some basic problems regarding a new learning culture using social networking software are discussed. Most of the educational institutions pay a lot of attentions to the equipments and emerging Information and Communication Technologies (ICTs) in learning situations. They try to incorporate ICT into their institutions as teaching and learning environments. They do this because they expect that by doing so they will improve the outcome of the learning process. Despite this, the learning outcome as reported in most studies is very limited, because the expectations of self-directed learning are much higher than the reality. Findings from an empirical study (investigating the role of teacher-learner interaction through new digital media wiki in higher education and learning outcome and learner’s satisfaction) are presented recommendations about the necessity of pedagogical interactions in support of teaching and learning activities in wiki courses in order to improve the learning outcome. Conclusions show the necessity for significant changes in the approach of vocational teacher training programs of online teachers in order to meet the requirements of new digital media in coherence with a new learning culture. These changes have to address collaborative instead of individual learning and ICT wiki as a tool for knowledge construction instead of a tool for gathering information.
This thesis contains several theoretical studies on optomechanical systems, i.e. physical devices where mechanical degrees of freedom are coupled with optical cavity modes. This optomechanical interaction, mediated by radiation pressure, can be exploited for cooling and controlling mechanical resonators in a quantum regime. The goal of this thesis is to propose several new ideas for preparing meso- scopic mechanical systems (of the order of 10^15 atoms) into highly non-classical states. In particular we have shown new methods for preparing optomechani-cal pure states, squeezed states and entangled states. At the same time, proce-dures for experimentally detecting these quantum effects have been proposed. In particular, a quantitative measure of non classicality has been defined in terms of the negativity of phase space quasi-distributions. An operational al- gorithm for experimentally estimating the non-classicality of quantum states has been proposed and successfully applied in a quantum optics experiment. The research has been performed with relatively advanced mathematical tools related to differential equations with periodic coefficients, classical and quantum Bochner’s theorems and semidefinite programming. Nevertheless the physics of the problems and the experimental feasibility of the results have been the main priorities.
A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.