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For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.
Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.
Organic semiconductors are a promising class of materials. Their special properties are the particularly good absorption, low weight and easy processing into thin films. Therefore, intense research has been devoted to the realization of thin film organic solar cells (OPVs). Because of the low dielectric constant of organic semiconductors, primary excitations (excitons) are strongly bound and a type II heterojunction needs to be introduced to split these excitations into free charges. Therefore, most organic solar cells consist of at least an electron donor and electron acceptor material. For such donor acceptor systems mainly three states are relevant; the photoexcited exciton on the donor or acceptor material, the charge transfer state at the donor-acceptor interface and the charge separated state of a free electron and hole. The interplay between these states significantly determines the efficiency of organic solar cells. Due to the high absorption and the low charge carrier mobilities, the active layers are usually thin but also, exciton dissociation and free charge formation proceeds rapidely, which makes the study of carrier dynamics highly challenging.
Therefore, the focus of this work was first to install new experimental setups for the investigation of the charge carrier dynamics in complete devices with superior sensitivity and time resolution and, second, to apply these methods to prototypical photovoltaic materials to address specific questions in the field of organic and hybrid photovoltaics.
Regarding the first goal, a new setup combining transient absorption spectroscopy (TAS) and time delayed collection field (TDCF) was designed and installed in Potsdam. An important part of this work concerned the improvement of the electronic components with respect to time resolution and sensitivity. To this end, a highly sensitive amplifier for driving and detecting the device response in TDCF was developed. This system was then applied to selected organic and hybrid model systems with a particular focus on the understanding of the loss mechanisms that limit the fill factor and short circuit current of organic solar cells.
The first model system was a hybrid photovoltaic material comprising inorganic quantum dots decorated with organic ligands. Measurements with TDCF revealed fast free carrier recombination, in part assisted by traps, while bias-assisted charge extraction measurements showed high mobility. The measured parameters then served as input for a successful description of the device performance with an analytical model.
With a further improvement of the instrumentation, a second topic was the detailed analysis of non-geminate recombination in a disordered polymer:fullerene blend where an important question was the effect of disorder on the carrier dynamics. The measurements revealed that early time highly mobile charges undergo fast non-geminate recombination at the contacts, causing an apparent field dependence of free charge generation in TDCF experiments if not conducted properly. On the other hand, recombination the later time scale was determined by dispersive recombination in the bulk of the active layer, showing the characteristics of carrier dynamics in an exponential density of state distribution. Importantly, the comparison with steady state recombination data suggested a very weak impact of non-thermalized carriers on the recombination properties of the solar cells under application relevant illumination conditions.
Finally, temperature and field dependent studies of free charge generation were performed on three donor-acceptor combinations, with two donor polymers of the same material family blended with two different fullerene acceptor molecules. These particular material combinations were chosen to analyze the influence of the energetic and morphology of the blend on the efficiency of charge generation. To this end, activation energies for photocurrent generation were accurately determined for a wide range of excitation energies. The results prove that the formation of free charge is via thermalized charge transfer states and does not involve hot exciton splitting. Surprisingly, activation energies were of the order of thermal energy at room temperature. This led to the important conclusion that organic solar cells perform well not because of predominate high energy pathways but because the thermalized CT states are weakly bound. In addition, a model is introduced to interconnect the dissociation efficiency of the charge transfer state with its recombination observable with photoluminescence, which rules out a previously proposed two-pool model for free charge formation and recombination. Finally, based on the results, proposals for the further development of organic solar cells are formulated.
Ultrafast magnetisation dynamics have been investigated intensely for two decades. The recovery process after demagnetisation, however, was rarely studied experimentally and discussed in detail. The focus of this work lies on the investigation of the magnetisation on long timescales after laser excitation. It combines two ultrafast time resolved methods to study the relaxation of the magnetic and lattice system after excitation with a high fluence ultrashort laser pulse. The magnetic system is investigated by time resolved measurements of the magneto-optical Kerr effect. The experimental setup has been implemented in the scope of this work. The lattice dynamics were obtained with ultrafast X-ray diffraction. The combination of both techniques leads to a better understanding of the mechanisms involved in magnetisation recovery from a non-equilibrium condition. Three different groups of samples are investigated in this work: Thin Nickel layers capped with nonmagnetic materials, a continuous sample of the ordered L10 phase of Iron Platinum and a sample consisting of Iron Platinum nanoparticles embedded in a carbon matrix. The study of the remagnetisation reveals a general trend for all of the samples: The remagnetisation process can be described by two time dependences. A first exponential recovery that slows down with an increasing amount of energy absorbed in the system until an approximately linear time dependence is observed. This is followed by a second exponential recovery. In case of low fluence excitation, the first recovery is faster than the second. With increasing fluence the first recovery is slowed down and can be described as a linear function. If the pump-induced temperature increase in the sample is sufficiently high, a phase transition to a paramagnetic state is observed. In the remagnetisation process, the transition into the ferromagnetic state is characterised by a distinct transition between the linear and exponential recovery. From the combination of the transient lattice temperature Tp(t) obtained from ultrafast X-ray measurements and magnetisation M(t) gained from magneto-optical measurements we construct the transient magnetisation versus temperature relations M(Tp). If the lattice temperature remains below the Curie temperature the remagnetisation curve M(Tp) is linear and stays below the M(T) curve in equilibrium in the continuous transition metal layers. When the sample is heated above phase transition, the remagnetisation converges towards the static temperature dependence. For the granular Iron Platinum sample the M(Tp) curves for different fluences coincide, i.e. the remagnetisation follows a similar path irrespective of the initial laser-induced temperature jump.
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called “autoinducers”) and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a “cluster” of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get “induced” into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.
In this work we investigated ultrafast demagnetization in a Heusler-alloy. This material belongs to the halfmetal and exists in a ferromagnetic phase. A special feature of investigated alloy is a structure of electronic bands. The last leads to the specific density of the states. Majority electrons form a metallic like structure while minority electrons form a gap near the Fermi-level, like in semiconductor. This particularity offers a good possibility to use this material as model-like structure and to make some proof of principles concerning demagnetization. Using pump-probe experiments we carried out time-resolved measurements to figure out the times of demagnetization. For the pumping we used ultrashort laser pulses with duration around 100 fs. Simultaneously we used two excitation regimes with two different wavelengths namely 400 nm and 1240 nm. Decreasing the energy of photons to the gap size of the minority electrons we explored the effect of the gap on the demagnetization dynamics. During this work we used for the first time OPA (Optical Parametrical Amplifier) for the generation of the laser irradiation in a long-wave regime. We tested it on the FETOSPEX-beamline in BASSYII electron storage ring. With this new technique we measured wavelength dependent demagnetization dynamics. We estimated that the demagnetization time is in a correlation with photon energy of the excitation pulse. Higher photon energy leads to the faster demagnetization in our material. We associate this result with the existence of the energy-gap for minority electrons and explained it with Elliot-Yaffet-scattering events. Additionally we applied new probe-method for magnetization state in this work and verified their effectivity. It is about the well-known XMCD (X-ray magnetic circular dichroism) which we adopted for the measurements in reflection geometry. Static experiments confirmed that the pure electronic dynamics can be separated from the magnetic one. We used photon energy fixed on the L3 of the corresponding elements with circular polarization. Appropriate incidence angel was estimated from static measurements. Using this probe method in dynamic measurements we explored electronic and magnetic dynamics in this alloy.
Membrane adhesion is a fundamental biological process in which membranes are attached to neighboring membranes or surfaces. Membrane adhesion emerges from a complex interplay between the binding of membrane-anchored receptors/ligands and the membrane properties. In this work, we study membrane adhesion mediated by lipid-anchored saccharides using microsecond-long full-atomistic molecular dynamics simulations. Motivated by neutron scattering experiments on membrane adhesion via lipid-anchored saccharides, we investigate the role of LeX, Lac1, and Lac2 saccharides and membrane fluctuations in membrane adhesion.
We study the binding of saccharides in three different systems: for saccharides in water, for saccharides anchored to essentially planar membranes at fixed separations, and for saccharides anchored to apposing fluctuating membranes. Our simulations of two saccharides in water indicate that the saccharides engage in weak interactions to form dimers. We find that the binding occurs in a continuum of bound states instead of a certain number of well-defined bound structures, which we term as "diffuse binding".
The binding of saccharides anchored to essentially planar membranes strongly depends on separation of the membranes, which is fixed in our simulation system. We show that the binding constants for trans-interactions of two lipid-anchored saccharides monotonically decrease with increasing separation. Saccharides anchored to the same membrane leaflet engage in cis-interactions with binding constants comparable to the trans-binding constants at the smallest membrane separations. The interplay of cis- and trans-binding can be investigated in simulation systems with many lipid-anchored saccharides. For Lac2, our simulation results indicate a positive cooperativity of trans- and cis-binding. In this cooperative binding the trans-binding constant is enhanced by the cis-interactions. For LeX, in contrast, we observe no cooperativity between trans- and cis-binding. In addition, we determine the forces generated by trans-binding of lipid-anchored saccharides in planar membranes from the binding-induced deviations of the lipid-anchors. We find that the forces acting on trans-bound saccharides increase with increasing membrane separation to values of the order of 10 pN.
The binding of saccharides anchored to the fluctuating membranes results from an interplay between the binding properties of the lipid-anchored saccharides and membrane fluctuations. Our simulations, which have the same average separation of the membranes as obtained from the neutron scattering experiments, yield a binding constant larger than in planar membranes with the same separation. This result demonstrates that membrane fluctuations play an important role at average membrane separations which are seemingly too large for effective binding. We further show that the probability distribution of the local separation can be well approximated by a Gaussian distribution. We calculate the relative membrane roughness and show that our results are in good agreement with the roughness values reported from the neutron scattering experiments.