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Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
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.
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.
R-Group stabilization in methylated formamides observed by resonant inelastic X-ray scattering
(2022)
The inherent stability of methylated formamides is traced to a stabilization of the deep-lying sigma-framework by resonant inelastic X-ray scattering at the nitrogen K-edge. Charge transfer from the amide nitrogen to the methyl groups underlie this stabilization mechanism that leaves the aldehyde group essentially unaltered and explains the stability of secondary and tertiary amides.
The subject of the present thesis is the one-dimensional Bose gas. Since long-rang order is destroyed by infra-red fluctuations in one dimension, only the formation of a quasi-condensate is possible, which exhibits suppressed density fluctuations, but whose phase fluctuates strongly. It is shown that modified mean-field theories based on a symmetry-breaking approach can even characterise phase coherence properties of such a quasi-condensate properly. A correct description of the transition from the degenerate ideal Bose gas to the quasi-condensate, which is a smooth cross-over rather than a phase transition, is not possible though. Basic conditions for the applicability of the theories are not fulfilled in this regime, such that the existence of a critical point is predicted.
The theories are compared on the basis of their excitation sprectum, equation of state, density fluctuations and related correlation functions. High-temperature expansions of the corresponding integrals are derived analytically for the numerical evaluation of the self-consistent integral equations. Apart from that, the Stochastic Gross-Pitaevskii equation (SGPE), a non-linear Langevin equation, is analysed numerically by means of Monte-Carlo simulations and the results are compared to those of the mean-field theories. In this context, a lot of attention is payed to the appropriate choice of the parameters. The simulations prove that the SGPE is capable of describing the cross-over properly, but highlight the limitations of the widely used local density approximation as well.
The Thesis is focused on the properties of self-organized nanostructures. Atomic and electronic properties of different systems have been investigated using methods of electron diffraction, scanning tunneling microscopy and photoelectron spectroscopy. Implementation of the STM technique (including design, construction, and tuning of the UHV experimental set-up) has been done in the framework of present work. This time-consuming work is reported to greater detail in the experimental part of this Thesis. The scientific part starts from the study of quantum-size effects in the electronic structure of a two-dimensional Ag film on the supporting substrate Ni(111). Distinct quantum well states in the sp-band of Ag were observed in photoelectron spectra. Analysis of thickness- and angle-dependent photoemission supplies novel information on the properties of the interface. For the first time the Ni(111) relative band gap was indirectly probed in the ground-state through the electronic structure of quantum well states in the adlayer. This is particularly important for Ni where valence electrons are strongly correlated. Comparison of the experiment with calculations performed in the formalism of the extended phase accumulation model gives the substrate gap which is fully consistent with the one obtained by ab-initio LDA calculations. It is, however, in controversy to the band structure of Ni measured directly by photoemission. These results lend credit to the simplest view of photoemission from Ni, assigning early observed contradictions between theory and experiments to electron correlation effects in the final state of photoemission. Further, nanosystems of lower dimensionality have been studied. Stepped surfaces W(331) and W(551) were used as one-dimensional model systems and as templates for self-organization of Au nanoclusters. Photon energy dependent photoemission revealed a surface resonance which was never observed before on W(110) which is the base plane of the terrace microsurfaces. The dispersion E(k) of this state measured on stepped W(331) and W(551) with angle-resolved photoelectron spectroscopy is modified by a strong umklapp effect. It appears as two parabolas shifted symmetrically relative to the microsurface normal by half of the Brillouin zone of the step superlattice. The reported results are very important for understanding of the electronic properties of low-dimensional nanostructures. It was also established that W(331) and W(551) can serve as templates for self-organization of metallic nanostructures. A combined study of electronic and atomic properties of sub-monolayer amounts of gold deposited on these templates have shown that if the substrate is slightly pre-oxidized and the temperature is elevated, then Au can alloy with the first monolayer of W. As a result, a nanostructure of uniform clusters of a surface alloy is produced all over the steps. Such clusters feature a novel sp-band in the vicinity of the Fermi level, which appears split into constant energy levels due to effects of lateral quantization. The last and main part of this work is devoted to large-scale reconstructions on surfaces and nanostructures self-assembled on top. The two-dimensional surface carbide W(110)/C-R(15x3) has been extensively investigated. Photoemission studies of quantum size effects in the electronic structure of this reconstruction, combined with an investigation of its surface geometry, lead to an advanced structural model of the carbide overlayer. It was discovered that W(110)/C-R(15x3) can control self-organization of adlayers into nanostructures with extremely different electronic and structural properties. Thus, it was established that at elevated temperature the R(15x3) superstructure controls the self-assembly of sub-monolayer amounts of Au into nm-wide nanostripes. Based on the results of core level photoemission, the R(15x3)-induced surface alloying which takes place between Au and W can be claimed as driving force of self-organization. The observed stripes exhibit a characteristic one-dimensional electronic structure with laterally quantized d-bands. Obviously, these are very important for applications, since dimensions of electronic devices have already stepped into the nm-range, where quantum-size phenomena must undoubtedly be considered. Moreover, formation of perfectly uniform molecular clusters of C60 was demonstrated and described in terms of the van der Waals formalism. It is the first experimental observation of two-dimensional fullerene nanoclusters with "magic numbers". Calculations of the cluster potentials using the static approach have revealed characteristic minima in the interaction energy. They are achieved for 4 and 7 molecules per cluster. The obtained "magic numbers" and the corresponding cluster structures are fully consistent with the results of the STM measurements.
Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus–Levich–Dogonadze(MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.
Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.
Recent progress towards a quantum theory of laser-induced desorption and related phenomena is reviewed, for specific examples. These comprise the photodesorption of NO from Pt(111), the scanning tunnelling microscope and laser- induced desorption and switching of H at Si(100), and the electron stimulated desorption and dissociation of CO at Ru(0001). The theoretical methods used for nuclear dynamics range from open-system density matrix theory over nonadiabatically coupled multi-state models to electron-nuclear wavepackets. Also, aspects of time-dependent spectroscopy to probe ultrafast nonadiabatic processes at surfaces will be considered for the example of two-photon photoemission of solvated electrons in ice layers on Cu(111)