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How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle’s motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.
There is a large variety of goals instructors have for laboratory courses, with different courses focusing on different subsets of goals. An often implicit, but crucial, goal is to develop students’ attitudes, views, and expectations about experimental physics to align with practicing experimental physicists. The assessment of laboratory courses upon this one dimension of learning has been intensively studied in U.S. institutions using the Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS). However, there is no such an instrument available to use in Germany, and the influence of laboratory courses on students views about the nature of experimental physics is still unexplored at German-speaking institutions. Motivated by the lack of an assessment tool to investigate this goal in laboratory courses at German-speaking institutions, we present a translated version of the E-CLASS adapted to the context at German-speaking institutions. We call the German version of the E-CLASS, the GE-CLASS. We describe the translation process and the creation of an automated web-based system for instructors to assess their laboratory courses. We also present first results using GE-CLASS obtained at the University of Potsdam. A first comparison between E-CLASS and GE-CLASS results shows clear differences between University of Potsdam and U.S. students’ views and beliefs about experimental physics.
We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal’s past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient’s beta-band brain activity.
Most of the matter in the universe consists of hydrogen. The hydrogen in the intergalactic medium (IGM), the matter between the galaxies, underwent a change of its ionisation state at the epoch of reionisation, at a redshift roughly between 6>z>10, or ~10^8 years after the Big Bang. At this time, the mostly neutral hydrogen in the IGM was ionised but the source of the responsible hydrogen ionising emission remains unclear. In this thesis I discuss the most likely candidates for the emission of this ionising radiation, which are a type of galaxy called Lyman alpha emitters (LAEs). As implied by their name, they emit Lyman alpha radiation, produced after a hydrogen atom has been ionised and recombines with a free electron. The ionising radiation itself (also called Lyman continuum emission) which is needed for this process inside the LAEs could also be responsible for ionising the IGM around those galaxies at the epoch of reionisation, given that enough Lyman continuum escapes. Through this mechanism, Lyman alpha and Lyman continuum radiation are closely linked and are both studied to better understand the properties of high redshift galaxies and the reionisation state of the universe.
Before I can analyse their Lyman alpha emission lines and the escape of Lyman continuum emission from them, the first step is the detection and correct classification of LAEs in integral field spectroscopic data, specifically taken with the Multi-Unit Spectroscopic Explorer (MUSE). After detecting emission line objects in the MUSE data, the task of classifying them and determining their redshift is performed with the graphical user interface QtClassify, which I developed during the work on this thesis. It uses the strength of the combination of spectroscopic and photometric information that integral field spectroscopy offers to enable the user to quickly identify the nature of the detected emission lines. The reliable classification of LAEs and determination of their redshifts is a crucial first step towards an analysis of their properties.
Through radiative transfer processes, the properties of the neutral hydrogen clouds in and around LAEs are imprinted on the shape of the Lyman alpha line. Thus after identifying the LAEs in the MUSE data, I analyse the properties of the Lyman alpha emission line, such as the equivalent width (EW) distribution, the asymmetry and width of the line as well as the double peak fraction. I challenge the common method of displaying EW distributions as histograms without taking the limits of the survey into account and construct a more independent EW distribution function that better reflects the properties of the underlying population of galaxies. I illustrate this by comparing the fraction of high EW objects between the two surveys MUSE-Wide and MUSE-Deep, both consisting of MUSE pointings (each with the size of one square arcminute) of different depths. In the 60 MUSE-Wide fields of one hour exposure time I find a fraction of objects with extreme EWs above EW_0>240A of ~20%, while in the MUSE-Deep fields (9 fields with an exposure time of 10 hours and one with an exposure time of 31 hours) I find a fraction of only ~1%, which is due to the differences in the limiting line flux of the surveys. The highest EW I measure is EW_0 = 600.63 +- 110A, which hints at an unusual underlying stellar population, possibly with a very low metallicity.
With the knowledge of the redshifts and positions of the LAEs detected in the MUSE-Wide survey, I also look for Lyman continuum emission coming from these galaxies and analyse the connection between Lyman continuum emission and Lyman alpha emission. I use ancillary Hubble Space Telescope (HST) broadband photometry in the bands that contain the Lyman continuum and find six Lyman continuum leaker candidates. To test whether the Lyman continuum emission of LAEs is coming only from those individual objects or the whole population, I select LAEs that are most promising for the detection of Lyman continuum emission, based on their rest-frame UV continuum and Lyman alpha line shape properties. After this selection, I stack the broadband data of the resulting sample and detect a signal in Lyman continuum with a significance of S/N = 5.5, pointing towards a Lyman continuum escape fraction of ~80%. If the signal is reliable, it strongly favours LAEs as the providers of the hydrogen ionising emission at the epoch of reionisation and beyond.
Microswimmers, i.e. swimmers of micron size experiencing low Reynolds numbers, have received a great deal of attention in the last years, since many applications are envisioned in medicine and bioremediation. A promising field is the one of magnetic swimmers, since magnetism is biocom-patible and could be used to direct or actuate the swimmers. This thesis studies two examples of magnetic microswimmers from a physics point of view.
The first system to be studied are magnetic cells, which can be magnetic biohybrids (a swimming cell coupled with a magnetic synthetic component) or magnetotactic bacteria (naturally occurring bacteria that produce an intracellular chain of magnetic crystals). A magnetic cell can passively interact with external magnetic fields, which can be used for direction. The aim of the thesis is to understand how magnetic cells couple this magnetic interaction to their swimming strategies, mainly how they combine it with chemotaxis (the ability to sense external gradient of chemical species and to bias their walk on these gradients). In particular, one open question addresses the advantage given by these magnetic interactions for the magnetotactic bacteria in a natural environment, such as porous sediments. In the thesis, a modified Active Brownian Particle model is used to perform simulations and to reproduce experimental data for different systems such as bacteria swimming in the bulk, in a capillary or in confined geometries. I will show that magnetic fields speed up chemotaxis under special conditions, depending on parameters such as their swimming strategy (run-and-tumble or run-and-reverse), aerotactic strategy (axial or polar), and magnetic fields (intensities and orientations), but it can also hinder bacterial chemotaxis depending on the system.
The second example of magnetic microswimmer are rigid magnetic propellers such as helices or random-shaped propellers. These propellers are actuated and directed by an external rotating magnetic field. One open question is how shape and magnetic properties influence the propeller behavior; the goal of this research field is to design the best propeller for a given situation. The aim of the thesis is to propose a simulation method to reproduce the behavior of experimentally-realized propellers and to determine their magnetic properties. The hydrodynamic simulations are based on the use of the mobility matrix. As main result, I propose a method to match the experimental data, while showing that not only shape but also the magnetic properties influence the propellers swimming characteristics.
Earth's climate varies continuously across space and time, but humankind has witnessed only a small snapshot of its entire history, and instrumentally documented it for a mere 200 years. Our knowledge of past climate changes is therefore almost exclusively based on indirect proxy data, i.e. on indicators which are sensitive to changes in climatic variables and stored in environmental archives. Extracting the data from these archives allows retrieval of the information from earlier times. Obtaining accurate proxy information is a key means to test model predictions of the past climate, and only after such validation can the models be used to reliably forecast future changes in our warming world. The polar ice sheets of Greenland and Antarctica are one major climate archive, which record information about local air temperatures by means of the isotopic composition of the water molecules embedded in the ice. However, this temperature proxy is, as any indirect climate data, not a perfect recorder of past climatic variations. Apart from local air temperatures, a multitude of other processes affect the mean and variability of the isotopic data, which hinders their direct interpretation in terms of climate variations. This applies especially to regions with little annual accumulation of snow, such as the Antarctic Plateau. While these areas in principle allow for the extraction of isotope records reaching far back in time, a strong corruption of the temperature signal originally encoded in the isotopic data of the snow is expected. This dissertation uses observational isotope data from Antarctica, focussing especially on the East Antarctic low-accumulation area around the Kohnen Station ice-core drilling site, together with statistical and physical methods, to improve our understanding of the spatial and temporal isotope variability across different scales, and thus to enhance the applicability of the proxy for estimating past temperature variability. The presented results lead to a quantitative explanation of the local-scale (1–500 m) spatial variability in the form of a statistical noise model, and reveal the main source of the temporal variability to be the mixture of a climatic seasonal cycle in temperature and the effect of diffusional smoothing acting on temporally uncorrelated noise. These findings put significant limits on the representativity of single isotope records in terms of local air temperature, and impact the interpretation of apparent cyclicalities in the records. Furthermore, to extend the analyses to larger scales, the timescale-dependency of observed Holocene isotope variability is studied. This offers a deeper understanding of the nature of the variations, and is crucial for unravelling the embedded true temperature variability over a wide range of timescales.
The Milky Way is only one out of billions of galaxies in the universe. However, it is a special galaxy because it allows to explore the main mechanisms involved in its evolution and formation history by unpicking the system star-by-star. Especially, the chemical fingerprints of its stars provide clues and evidence of past events in the Galaxy’s lifetime. These information help not only to decipher the current structure and building blocks of the Milky Way, but to learn more about the general formation process of galaxies.
In the past decade a multitude of stellar spectroscopic Galactic surveys have scanned millions of stars far beyond the rim of the solar neighbourhood. The obtained spectroscopic information provide unprecedented insights to the chemo-dynamics of the Milky Way. In addition analytic models and numerical simulations of the Milky Way provide necessary descriptions and predictions suited for comparison with observations in order to decode the physical properties that underlie the complex system of the Galaxy.
In the thesis various approaches are taken to connect modern theoretical modelling of galaxy formation and evolution with observations from Galactic stellar surveys. With its focus on the chemo-kinematics of the Galactic disk this work aims to determine new observational constraints on the formation of the Milky Way providing also proper comparisons with two different models. These are the population synthesis model TRILEGAL based on analytical distribution functions, which aims to simulate the number and distribution of stars in the Milky Way and its different components, and a hybrid model (MCM) that combines an N-body simulation of a Milky Way like galaxy in the cosmological framework with a semi-analytic chemical evolution model for the Milky Way. The major observational data sets in use come from two surveys, namely the “Radial Velocity Experiment” (RAVE) and the “Sloan Extension for Galactic Understanding and Exploration” (SEGUE).
In the first approach the chemo-kinematic properties of the thin and thick disk of the Galaxy as traced by a selection of about 20000 SEGUE G-dwarf stars are directly compared to the predictions by the MCM model. As a necessary condition for this, SEGUE's selection function and its survey volume are evaluated in detail to correct the spectroscopic observations for their survey specific selection biases. Also, based on a Bayesian method spectro-photometric distances with uncertainties below 15% are computed for the selection of SEGUE G-dwarfs that are studied up to a distance of 3 kpc from the Sun.
For the second approach two synthetic versions of the SEGUE survey are generated based on the above models. The obtained synthetic stellar catalogues are then used to create mock samples best resembling the compiled sample of observed SEGUE G-dwarfs. Generally, mock samples are not only ideal to compare predictions from various models. They also allow validation of the models' quality and improvement as with this work could be especially achieved for TRILEGAL. While TRILEGAL reproduces the statistical properties of the thin and thick disk as seen in the observations, the MCM model has shown to be more suitable in reproducing many chemo-kinematic correlations as revealed by the SEGUE stars. However, evidence has been found that the MCM model may be missing a stellar component with the properties of the thick disk that the observations clearly show. While the SEGUE stars do indicate a thin-thick dichotomy of the stellar Galactic disk in agreement with other spectroscopic stellar studies, no sign for a distinct metal-poor disk is seen in the MCM model.
Usually stellar spectroscopic surveys are limited to a certain volume around the Sun covering different regions of the Galaxy’s disk. This often prevents to obtain a global view on the chemo-dynamics of the Galactic disk. Hence, a suitable combination of stellar samples from independent surveys is not only useful for the verification of results but it also helps to complete the picture of the Milky Way. Therefore, the thesis closes with a comparison of the SEGUE G-dwarfs and a sample of RAVE giants. The comparison reveals that the chemo-kinematic relations agree in disk regions where the samples of both surveys show a similar number of stars. For those parts of the survey volumes where one of the surveys lacks statistics they beautifully complement each other. This demonstrates that the comparison of theoretical models on the one side, and the combined observational data gathered by multiple surveys on the other side, are key ingredients to understand and disentangle the structure and formation history of the Milky Way.
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.