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- Institut für Physik und Astronomie (20) (remove)
The Sun is surrounded by a 10^6 K hot atmosphere, the corona. The corona and the solar wind are fully ionized, and therefore in the plasma state. Magnetic fields play an important role in a plasma, since they bind electrically charged particles to their field lines. EUV spectroscopes, like the SUMER instrument on-board the SOHO spacecraft, reveal a preferred heating of coronal ions and strong temperature anisotropies. Velocity distributions of electrons can be measured directly in the solar wind, e.g. with the 3DPlasma instrument on-board the WIND satellite. They show a thermal core, an anisotropic suprathermal halo, and an anti-solar, magnetic-field-aligned, beam or "strahl". For an understanding of the physical processes in the corona, an adequate description of the plasma is needed. Magnetohydrodynamics (MHD) treats the plasma simply as an electrically conductive fluid. Multi-fluid models consider e.g. protons and electrons as separate fluids. They enable a description of many macroscopic plasma processes. However, fluid models are based on the assumption of a plasma near thermodynamic equilibrium. But the solar corona is far away from this. Furthermore, fluid models cannot describe processes like the interaction with electromagnetic waves on a microscopic scale. Kinetic models, which are based on particle velocity distributions, do not show these limitations, and are therefore well-suited for an explanation of the observations listed above. For the simplest kinetic models, the mirror force in the interplanetary magnetic field focuses solar wind electrons into an extremely narrow beam, which is contradicted by observations. Therefore, a scattering mechanism must exist that counteracts the mirror force. In this thesis, a kinetic model for electrons in the solar corona and wind is presented that provides electron scattering by resonant interaction with whistler waves. The kinetic model reproduces the observed components of solar wind electron distributions, i.e. core, halo, and a "strahl" with finite width. But the model is not only applicable on the quiet Sun. The propagation of energetic electrons from a solar flare is studied, and it is found that scattering in the direction of propagation and energy diffusion influence the arrival times of flare electrons at Earth approximately to the same degree. In the corona, the interaction of electrons with whistler waves does not only lead to scattering, but also to the formation of a suprathermal halo, as it is observed in interplanetary space. This effect is studied both for the solar wind as well as the closed volume of a coronal magnetic loop. The result is of fundamental importance for solar-stellar relations. The quiet solar corona always produces suprathermal electrons. This process is closely related to coronal heating, and can therefore be expected in any hot stellar corona. In the second part of this thesis it is detailed how to calculate growth or damping rates of plasma waves from electron velocity distributions. The emission and propagation of electron cyclotron waves in the quiet solar corona, and that of whistler waves during solar flares, is studied. The latter can be observed as so-called fiber bursts in dynamic radio spectra, and the results are in good agreement with observed bursts.
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.
Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics
(2012)
Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples.
One of the most exciting predictions of Einstein's theory of gravitation that have not yet been proven experimentally by a direct detection are gravitational waves. These are tiny distortions of the spacetime itself, and a world-wide effort to directly measure them for the first time with a network of large-scale laser interferometers is currently ongoing and expected to provide positive results within this decade. One potential source of measurable gravitational waves is the inspiral and merger of two compact objects, such as binary black holes. Successfully finding their signature in the noise-dominated data of the detectors crucially relies on accurate predictions of what we are looking for. In this thesis, we present a detailed study of how the most complete waveform templates can be constructed by combining the results from (A) analytical expansions within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches for nonspinning systems by extending the accessible parameter space and introducing an alternative scheme based in the Fourier domain. Our methods can now be readily applied to multiple spherical-harmonic modes and precessing systems. In addition to that, we analyze in detail the accuracy of hybrid waveforms with the goal to quantify how numerous sources of error in the approximation techniques affect the application of such templates in real gravitational-wave searches. This is of major importance for the future construction of improved models, but also for the correct interpretation of gravitational-wave observations that are made utilizing any complete waveform family. In particular, we comprehensively discuss how long the numerical-relativity contribution to the signal has to be in order to make the resulting hybrids accurate enough, and for currently feasible simulation lengths we assess the physics one can potentially do with template-based searches.
We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis.
Actin is one of the most abundant and highly conserved proteins in eukaryotic cells. The globular protein assembles into long filaments, which form a variety of different networks within the cytoskeleton. The dynamic reorganization of these networks - which is pivotal for cell motility, cell adhesion, and cell division - is based on cycles of polymerization (assembly) and depolymerization (disassembly) of actin filaments. Actin binds ATP and within the filament, actin-bound ATP is hydrolyzed into ADP on a time scale of a few minutes. As ADP-actin dissociates faster from the filament ends than ATP-actin, the filament becomes less stable as it grows older. Recent single filament experiments, where abrupt dynamical changes during filament depolymerization have been observed, suggest the opposite behavior, however, namely that the actin filaments become increasingly stable with time. Several mechanisms for this stabilization have been proposed, ranging from structural transitions of the whole filament to surface attachment of the filament ends. The key issue of this thesis is to elucidate the unexpected interruptions of depolymerization by a combination of experimental and theoretical studies. In new depolymerization experiments on single filaments, we confirm that filaments cease to shrink in an abrupt manner and determine the time from the initiation of depolymerization until the occurrence of the first interruption. This duration differs from filament to filament and represents a stochastic variable. We consider various hypothetical mechanisms that may cause the observed interruptions. These mechanisms cannot be distinguished directly, but they give rise to distinct distributions of the time until the first interruption, which we compute by modeling the underlying stochastic processes. A comparison with the measured distribution reveals that the sudden truncation of the shrinkage process neither arises from blocking of the ends nor from a collective transition of the whole filament. Instead, we predict a local transition process occurring at random sites within the filament. The combination of additional experimental findings and our theoretical approach confirms the notion of a local transition mechanism and identifies the transition as the photo-induced formation of an actin dimer within the filaments. Unlabeled actin filaments do not exhibit pauses, which implies that, in vivo, older filaments become destabilized by ATP hydrolysis. This destabilization can be identified with an acceleration of the depolymerization prior to the interruption. In the final part of this thesis, we theoretically analyze this acceleration to infer the mechanism of ATP hydrolysis. We show that the rate of ATP hydrolysis is constant within the filament, corresponding to a random as opposed to a vectorial hydrolysis mechanism.
This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.
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.
Estimation of the self-similarity exponent has attracted growing interest in recent decades and became a research subject in various fields and disciplines. Real-world data exhibiting self-similar behavior and/or parametrized by self-similarity exponent (in particular Hurst exponent) have been collected in different fields ranging from finance and human sciencies to hydrologic and traffic networks. Such rich classes of possible applications obligates researchers to investigate qualitatively new methods for estimation of the self-similarity exponent as well as identification of long-range dependencies (or long memory). In this thesis I present the Bayesian estimation of the Hurst exponent. In contrast to previous methods, the Bayesian approach allows the possibility to calculate the point estimator and confidence intervals at the same time, bringing significant advantages in data-analysis as discussed in this thesis. Moreover, it is also applicable to short data and unevenly sampled data, thus broadening the range of systems where the estimation of the Hurst exponent is possible. Taking into account that one of the substantial classes of great interest in modeling is the class of Gaussian self-similar processes, this thesis considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed.
In the context of cosmological structure formation sheets, filaments and eventually halos form due to gravitational instabilities. It is noteworthy, that at all times, the majority of the baryons in the universe does not reside in the dense halos but in the filaments and the sheets of the intergalactic medium. While at higher redshifts of z > 2, these baryons can be detected via the absorption of light (originating from more distant sources) by neutral hydrogen at temperatures of T ~ 10^4 K (the Lyman-alpha forest), at lower redshifts only about 20 % can be found in this state. The remain (about 50 to 70 % of the total baryons mass) is unaccounted for by observational means. Numerical simulations predict that these missing baryons could reside in the filaments and sheets of the cosmic web at high temperatures of T = 10^4.5 - 10^7 K, but only at low to intermediate densities, and constitutes the warm-hot intergalactic medium (WHIM). The high temperatures of the WHIM are caused by the formation of shocks and the subsequent shock-heating of the gas. This results in a high degree of ionization and renders the reliable detection of the WHIM a challenging task. Recent high-resolution hydrodynamical simulations indicate that, at redshifts of z ~ 2, filaments are able to provide very massive galaxies with a significant amount of cool gas at temperatures of T ~ 10^4 K. This could have an important impact on the star-formation in those galaxies. It is therefore of principle importance to investigate the particular hydro- and thermodynamical conditions of these large filament structures. Density and temperature profiles, and velocity fields, are expected to leave their special imprint on spectroscopic observations. A potential multiphase structure may act as tracer in observational studies of the WHIM. In the context of cold streams, it is important to explore the processes, which regulate the amount of gas transported by the streams. This includes the time evolution of filaments, as well as possible quenching mechanisms. In this context, the halo mass range in which cold stream accretion occurs is of particular interest. In order to address these questions, we perform particular hydrodynamical simulations of very high resolution, and investigate the formation and evolution of prototype structures representing the typical filaments and sheets of the WHIM. We start with a comprehensive study of the one-dimensional collapse of a sinusoidal density perturbation (pancake formation) and examine the influence of radiative cooling, heating due to an UV background, thermal conduction, and the effect of small-scale perturbations given by the cosmological power spectrum. We use a set of simulations, parametrized by the wave length of the initial perturbation L. For L ~ 2 Mpc/h the collapse leads to shock-confined structures. As a result of radiative cooling and of heating due to an UV background, a relatively cold and dense core forms. With increasing L the core becomes denser and more concentrated. Thermal conduction enhances this trend and may lead to an evaporation of the core at very large L ~ 30 Mpc/h. When extending our simulations into three dimensions, instead of a pancake structure, we obtain a configuration consisting of well-defined sheets, filaments, and a gaseous halo. For L > 4 Mpc/h filaments form, which are fully confined by an accretion shock. As with the one-dimensional pancakes, they exhibit an isothermal core. Thus, our results confirm a multiphase structure, which may generate particular spectral tracers. We find that, after its formation, the core becomes shielded against further infall of gas onto the filament, and its mass content decreases with time. In the vicinity of the halo, the filament's core can be attributed to the cold streams found in other studies. We show, that the basic structure of these cold streams exists from the very beginning of the collapse process. Further on, the cross section of the streams is constricted by the outwards moving accretion shock of the halo. Thermal conduction leads to a complete evaporation of the cold stream for L > 6 Mpc/h. This corresponds to halos with a total mass higher than M_halo = 10^13 M_sun, and predicts that in more massive halos star-formation can not be sustained by cold streams. Far away from the gaseous halo, the temperature gradients in the filament are not sufficiently strong for thermal conduction to be effective.