Machine learning has recently made significant progress due to modern neural network architectures and training procedures. When neural networks learn a task, they create internal representations of the input data. The specific neural network architecture, training process, and task being addressed will influence the way in which the neural network interprets and explains the patterns in the data. The goal of representation learning is to train the neural network to create representations that effectively capture the overall structure of the data. However, the process by which these representations are generated is not fully understood because of the complexity of neural network data manipulations. This makes it difficult to choose the correct training procedure in real world applications. In this dissertation, we apply representation learning to improve the performance of neural networks in three different areas: NBA movement data, material property prediction, and generative protein modeling. First, we propose a novel deep learning approach for predicting human trajectories in sporting events using advanced object tracking data. Our method leverages recent advances in deep learning techniques, including the use of recurrent neural networks and long short-term memory cells, to accurately predict the future movements of players and the ball in a basketball game. We evaluate our approach using data from the NBA's advanced object tracking system and demonstrate improved performance compared to existing methods. Our results have the potential to inform real-time decision making in sports analytics and improve the understanding of player behavior and strategy. Next, we focused on group activity recognition (GAR) in basketball. In basketball, players engage in various activities, both collaborative and adversarial, in order to win the game. Identifying and analyzing these activities is important for sports analytics as it can inform better strategies and decisions by players and coaches. We introduce a novel deep learning approach for GAR in team sports called NETS. NETS utilizes a Transformer-based architecture combined with LSTM embedding and a team-wise pooling layer to recognize group activity. We test NETS using tracking data from 632 NBA games and found that it was able to learn group activities with high accuracy. Additionally, self- and weak-supervised training in NETS improved the accuracy of GAR. Then, study an application of neural networks on protein modeling. Recent work on autoregressive direct coupling analysis (arDCA) has shown promising potential to efficiently train a generative protein sequence model (GPSM) to adequately model protein sequence data. We propose an extension to this work by adding a higher order coupling estimator to build a model called autoregressive higher order coupling analysis (arHCA). We show that our model can correctly identify higher order couplings in a synthetic dataset and that our model improves the performance of arDCA when trained on real-world sequence data. Finally, we study material property prediction. Incorporation of physical principles in a machine learning (ML) architecture is a fundamental step toward the continued development of AI for inorganic materials. As inspired by the Pauling’s rule, we propose that structure motifs in inorganic crystals can serve as a central input to a machine learning framework. To demonstrate the use of structure motif information, a motif-centric learning framework is created by combining motif information with the atom-based graph neural networks to form an atom-motif dual graph network (AMDNet), which is more accurate in predicting the electronic structures of metal oxides such as bandgaps. The work illustrates the route toward fundamental design of graph neural network learning architecture for complex materials by incorporating beyond-atom physical principles. / Computer and Information Science

Although semilocal density functional approximations (DFA) are widely applied, none of them can capture the long-range van der Waals (vdW) attraction between the separated subsystems. However, they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly-constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semi-local functionals require an additive correction like non-local correlation functionals (vdW-DFs, VV10, rVV10 etc.) or empirical methods ( DFT+D3, DFT+vdW, DFT+XDM etc.) to capture the long-range part. The molecular complexes bonded by vdW interactions, layered materials, and molecule-surface interactions are a few examples of the systems where the long-range effects play a crucial role.In the first part of this assessment, we investigate the adsorption of benzene and thiophene over the (111) surface of copper (Cu), gold (Au), and silver (Ag). Thiophene and benzene are the prototypes of their respective classes of aromatic compounds and are the most widely studied molecules to model such systems. We first combine a non-local correlation functional (rVV10) with the various generalized gradient approximations (GGAs), namely PBE and PBEsol, along with the meta-GGAs SCAN and revSCAN (collectively known as base functionals), through a set of parameters obtained by fitting against the argon-dimer interaction energy curve. These parameters bridge the base functionals and rVV10 and guide the delicate balance between the short- and long-range interaction. We also utilize the recently introduced vdW-dZK model based on the theory of Zaremba and Kohn. It is a proven method to yield RPA-quality results for the physisorption of graphene over different metallic surfaces. We assess the adsorption energies, vertical adsorption distances, and the molecular-orientation at various sites and compare the results to the experimental values whenever available. Based on our calculations, the semilocal functionals alone underestimate the adsorption energies, reflecting the need for additional corrections. The rVV10-based methods generally bring the molecules closer to the surface and increase the binding energies. However, there is a discrepancy in the description of rVV10 based methods when the base functional is changed. While rVV10 combined with PBE slightly underestimates the adsorption energies, revSCAN+rVV10 and PBEsol+rVV10 are significantly overestimating. The methods PBE+vdW-dZK and SCAN+vdW-dZK, in general, predict better adsorption energies. In particular, SCAN+vdW-dZK stands out in predicting adsorption distances, adsorption energies, sites, and orientation closest to the experimental values whenever available. Apart from the inability of the semilocal DFAs to capture the long-range vdW interaction, they suffer from the so-called self-interaction error (SIE), in which an electron density incorrectly interacts with itself. At the semilocal level, the self-exchange-correlation energy can not counter-balance the self-Hartree energy, giving rise to the SIE problem. About 40 years ago, Perdew and Zunger proposed a solution to it by introducing a method that could remove the spurious SIE on an orbital-by-orbital basis. However, for size-consistency of this orbital-dependent theory, localized orbitals instead of delocalized Kohn-Sham orbitals are required. Recently, Pederson \textit{et al.} introduced an elegant scheme, known as Fermi-L\"owdin orbital self-interaction correction (FLOSIC), which could generate size-extensive and localized orbitals. For an exact functional, free from SIE, the negative of the highest occupied orbital (HO) eigenvalue would equal the first ionization energy (IE). In the second part of this assessment, we evaluate the HO eigenvalue of a representative test set containing 14 small to moderate-sized organic molecules using FLOSIC. The SIE inherent in the semilocal DFAs seriously underestimates the magnitude of the HO energy. Although LDA-SIC and PBE-SIC correct them, IEs are still significantly overestimated. A similar previous work by Vydrov \textit{et al.} reported the over-correction of PZ-SIC in many-electron regions, and various schemes with moderate success have been introduced since then to scale SIC down on those regions. Recently Zope \textit{et al.} introduced a method (LSIC) based on locally scaling-down PZ-SIC using an iso-orbital indicator (z$_\sigma$) which ensures that the correction is made only in the regions where they are required. We introduce a few other approaches similar to LSIC and demonstrate that these methods significantly improve the agreement between the calculated HO eigenvalues and experimental IEs of molecules. / Physics

Hadron structure is an important field in particle physics because hadrons make up most of the matter in nature. The theory of the strong nuclear force, via which the partons of hadrons interact, is Quantum Chromodynamics (QCD) and cannot be solved analytically. Lattice QCD (LQCD) is an ideal formulation of QCD and is the only formulation starting from first principles. In this thesis, we use LQCD for two primary topics of study: 1) nucleon structure and 2) pion and kaon structure. In the first study, we calculate the quark momentum fraction, helicity, and transversity for the nucleon. The calculations are performed on three ensembles at the physical point of the pion mass allowing us to study finite volume, discretization, strange and charm quark quenching, and excited-state systematic effects. Our calculations of the helicity and transversity are first predictions at the physical point. In the second study, we investigate pion and kaon structure. We calculate the first three non-trivial Mellin moments of the meson parton distribution functions (PDFs). For the kaon, this is the first direct calculation of the second and third moments. We carefully choose which matrix elements we implement so that there is no mixing with lower derivative operators, avoiding systematic uncertainties which are not well understood. We also perform an extensive study of the excited-state contamination. In a pioneering study, we show that the full x-dependence of the PDFs can be calculated from the first three Mellin moments. Such a calculation was previously thought to be unfeasible using moments calculated from LQCD. Our reconstruction of the PDFs allow us to comment on SU(3) flavor symmetry breaking and the high-x behavior of the pion PDF which are both interesting topics in hadron structure. / Physics

This thesis aims to theoretically explore the geometrical effects on spin waves, the fundamental low-energy excitations of ferromagnets, propagating in curved magnetic shells. Supported by an efficient numerical technique developed for this thesis, several aspects of curvilinear spin-wave dynamics involving magnetic pseudo-charges, the topology of curved magnets, symmetry-breaking effects, and dynamics of spin textures are studied. In recent years, geometrical and curvature effects on mesoscale ferromagnets have attracted the attention of fundamental and applied research. Exciting curvature-induced phenomena include chiral symmetry breaking, the stabilization of magnetic skyrmions on Gaussian bumps, or topologically induced domain walls in Möbius ribbons. Spin waves in vortex-state magnetic nanotubes exhibit a curvature-induced dispersion asymmetry due to geometric contributions to the magnetic volume pseudo-charges. However, previous theoretical studies were limited to simple and thin curved shells due to the complexity of analytical models and the time-consuming nature of existing numerical techniques. For a systematic study of spin-wave propagation in curved shells, the first of five thematic parts of this thesis deals with developing a numerical method to calculate spin-wave spectra in waveguides with arbitrarily shaped cross-sections efficiently. For this, a finite-element/boundary-element method to calculate dynamic dipolar fields, the Fredkin-Koehler method, was extended for propagating waves. The technique is implemented in the micromagnetic modeling package TetraX developed and made available as open source to the scientific community. Equipped with this method, the second part of the thesis studies the influence of geometric contributions to the magnetic charges leading to nonlocal chiral symmetry breaking. Introducing the toroidal moment to spin-wave dynamics allows us to predict whether this symmetry breaking is present even in complicated systems with spatially inhomogeneous equilibria or shells with gradient curvatures. The theoretical study of curvilinear magnetism is extended to thick shells, uncovering a curvature-induced nonreciprocity in the spatial mode profiles of the spin waves. Consequently, nonreciprocal dipole-dipole hybridization between different modes leads to asymmetric level gaps enabling spin-wave diode behavior. Besides unidirectional transport, curvature modifies the weakly nonlinear spin-wave interactions. The third part of this thesis focuses on topological effects. A topological Berry phase of spin waves in helical-state nanotubes is studied and connected to a local curvature-induced chiral interaction of exchange origin. The topology of more complicated systems, such as magnetic Möbius ribbons, is shown to impose selection rules on the spectrum of possible spin waves and split it into modes with half and full-integer indices. To understand the effects of achiral symmetry breaking, the fourth part of this thesis focuses on the deformation of symmetric shells, here, cylindrical nanotubes, to polygonal and elliptical shapes. Lowering rotational symmetry leads to splitting spin-wave dispersions into singlet and doublets branches, which is explained using a simple group theory approach and is analogous to the electron band structure in crystals. Apart from mode splitting, this symmetry breaking allows hybridization between different spin-wave modes and modifies their microwave absorption. While this hybridization appears discretely in polygonal tubes, tuning the eccentricity of elliptical tubes allows controlling the level gaps appearing from hybridization. Finally, the last part focuses on the dynamics of spin waves in the vicinity of spin textures in curvilinear systems. The dynamics of topological meron strings are shown to exhibit dipole-induced chiral symmetry breaking like spin waves in curved shells. Moreover, modulational instability is predicted from the softening of their gyrotropic modes, similar to the formation of stripe domains in flat systems. This stripe domain formation can also be observed in curved shells but leads to tilted or helix domains. Overall, this thesis contributes to the fundamental understanding of spin-wave dynamics on the mesoscale but also advertises these for possible magnonic applications.:Abstract Acknowledgements Contents 1 Introduction Theoretical Foundations 2 Micromagnetic continuum theory 3 Spin waves Numerical methods in micromagnetism 4 Overview 5 Finite-element dynamic-matrix method for propagating spin waves 6 Numerical reverse-engineering of spin-wave dispersions 7 TetraX: A micromagnetic modeling package Aspects of curvilinear magnetization dynamics 8 Magnetic charges 9 Topology 10 Achiral symmetry breaking 11 Spin textures Closing remarks 12 Summary and outlook 13 Publications and conference contributions Appendix A Extended derivations and proofs B Supplementary data and discussion List of Figures List of Tables Bibliography Alphabetical Index / Ziel dieser Arbeit ist es, die geometrischen Effekte auf Spinwellen (Magnonen), die fundamentalen niederenergetischen Anregungen von Ferromagneten, die sich in gekrümmten magnetischen Schalen ausbreiten, theoretisch zu untersuchen. Unterstützt durch ein effizientes numerisches Verfahren, das für diese Arbeit entwickelt wurde, werden verschiedene Aspekte der krummlinigen Spinwellen-Dynamik untersucht: magnetische Pseudoladungen, die Topologie gekrümmter Magnete, Symmetriebrechungseffekte und die Dynamik von Spin-Texturen. In den letzten Jahren haben Geometrie- und Krümmungseffekte auf mesoskaligen Ferromagneten die Aufmerksamkeit der Grundlagen- und angewandten Forschung auf sich gezogen. Zu den spannenden krümmungsinduzierten Phänomenen gehören chirale Symmetriebrechung, die Stabilisierung magnetischer Skyrmionen auf Gaußschen Unebenheiten oder topologisch induzierte Domänenwände in Möbiusbändern. Spinwellen in magnetischen Nanoröhren im Vortex-Zustand zeigen eine krümmungsinduzierte Dispersionsasymmetrie aufgrund geometrischer Beiträge zu den magnetischen Volumen-Pseudoladungen. Bisherige theoretische Studien beschränkten sich jedoch auf einfache und dünne gekrümmte Schalen, da die analytischen Modelle zu komplex und die bestehenden numerischen Verfahren zu zeitaufwändig waren. Für eine systematische Untersuchung der Spinwellenausbreitung in gekrümmten Schalen befasst sich der erste von fünf thematischen Teilen dieser Arbeit mit der Entwicklung einer numerischen Methode zur effizienten Berechnung von Spinwellenspektren in Wellenleitern mit beliebig geformten Querschnitten. Dazu wurde eine Finite-Elemente/Grenzelement-Methode zur Berechnung dynamischer Dipolfelder, die Fredkin-Köhler-Methode, für propagierende Wellen erweitert. Die Technik ist in dem mikromagnetischen Modellierungspaket TetraX implementiert, das während dieser Arbeit entwickelt und der wissenschaftlichen Gemeinschaft als Open Source zur Verfügung gestellt wurde. Ausgestattet mit dieser Methode untersucht der zweite Teil der Arbeit den Einfluss von geometrischen Beiträgen zu den magnetischen Ladungen, die zu nichtlokaler chiraler Symmetriebrechung führen. Durch die Einführung des toroidalen Moments in die Spin-Wellen-Dynamik lässt sich vorhersagen, ob diese Symmetriebrechung auch in komplizierten Systemen mit räumlich inhomogenen Gleichgewichtszuständen oder magnetischen Schalen mit Gradientenkrümmungen vorhanden ist. Die theoretische Untersuchung des krummlinigen Magnetismus wird auf dicke Schalen ausgedehnt, für die eine krümmungsbedingte Nichtreziprozität in den räumlichen Modenprofilen der Spinwellen gefunden wird. Als Konsequenz führt nicht-reziproke Dipol-Dipol-Hybridisierung zwischen verschiedenen Moden zu asymmetrischen Niveaulücken, die die Konstruktion von Spinwellen-Dioden ermöglichen. Neben unidirektionalem Transport modifiziert die Krümmung auch die schwach nichtlinearen Spin-Wellen-Wechselwirkungen. Der dritte Teil dieser Arbeit befasst sich mit topologischen Effekten. So wird eine topologische Berry-Phase von Spinwellen in Nanoröhren im Helix-Zustand untersucht, die mit einer lokalen krümmungsinduzierten chiralen Wechselwirkung in Verbindung gebracht wird. Es wird gezeigt, dass die Topologie komplizierterer Systeme, wie z.B. magnetischer Möbiusbänder, dem Spektrum möglicher Spinwellen Auswahlsregeln auferlegt, das damit in Moden mit halb- und ganzzahligen Indizes aufspaltet. Um die Auswirkungen der achiralen Symmetriebrechung zu verstehen, konzentriert sich der vierte Teil dieser Arbeit auf die Verformung symmetrischer Schalen, hier zylindrischer Nanoröhren, zu polygonalen und elliptischen Formen. Die Verringerung der Rotationssymmetrie führt zu einer Aufspaltung der Spin-Wellen-Dispersionen in Singlets Dublets, was mit einem einfachen gruppentheoretischen Ansatz erklärt wird und analog zur Elektronenbandstruktur in Kristallen ist. Abgesehen von der Modenaufspaltung ermöglicht diese Symmetriebrechung eine Hybridisierung zwischen verschiedenen Spin-Wellen-Moden und verändert zudem deren Mikrowellenabsorption. Während diese Hybridisierung in polygonalen Röhren diskret auftritt, kann die Exzentrizität elliptischer Röhren genutzt werden um die durch Hybridisierung entstehenden Niveaulücken kontinuierlich einzustellen. Schließlich konzentriert sich der letzte Teil auf die Dynamik von Spinwellen in der Umgebung von Spinstrukturen in krummlinigen Systemen. Es wird gezeigt, dass die Dynamik topologischer Meron-Strings dipol-induzierte chirale Symmetriebrechungen wie Spinwellen in gekrümmten Schalen aufweist. Darüber hinaus wird eine Instabilität der gyrotropen Mode vorhergesagt, ähnlich der Bildung von Streifendomänen in flachen Systemen. Diese Bildung von Streifendomänen kann auch in gekrümmten Schalen beobachtet werden, führt aber zu gekippten oder spiralförmigen Domänen. Insgesamt trägt diese Arbeit zum grundlegenden Verständnis der Spinnwellen-Dynamik auf der Mesoskala bei, aber diskutiert auch mögliche magnonische Anwendungen.:Abstract Acknowledgements Contents 1 Introduction Theoretical Foundations 2 Micromagnetic continuum theory 3 Spin waves Numerical methods in micromagnetism 4 Overview 5 Finite-element dynamic-matrix method for propagating spin waves 6 Numerical reverse-engineering of spin-wave dispersions 7 TetraX: A micromagnetic modeling package Aspects of curvilinear magnetization dynamics 8 Magnetic charges 9 Topology 10 Achiral symmetry breaking 11 Spin textures Closing remarks 12 Summary and outlook 13 Publications and conference contributions Appendix A Extended derivations and proofs B Supplementary data and discussion List of Figures List of Tables Bibliography Alphabetical Index

The Random Phase Approximation and beyond Random Phase Approximation methods based on Adiabatic Connection Fluctuation Dissipation Theorem (ACFD) are tested for structural phase transitions of different groups of materials, including metal to metal, metal to semiconductor, semiconductor to semiconductor transitions. Also the performance assessment of semilocal density functionals with or without empirical long range dispersion corrections has been explored for the same cases. We have investigated the structural phase transitions of three broad group of materials, semi- conductor to metal transitions involving two symmetric structures, semiconductor to metal and wide bandgap semiconductor to semiconductor transitions involving at least one lower symmetric structure and lastly special cases comprising metal to metal transitions and transitions between energetically very close structural phases. The first group contains Si (diamond → β-tin), Ge (diamond → β-tin) and SiC (zinc blende → rocksalt), second group contains GaAs (zinc blende → cmcm) and SiO 2 (quartz → stishovite) and third group contains Pb (fcc → hcp), C(graphite → diamond) and BN (cubic → hexagonal) respectively. We have found that the difference in behavior of exchange and correlation in semilocal functionals and ACFD methods is striking. For the former, the exchange potential and energy often comprise the majority of the binding described by density functional approximations, and the addition of the correlation energy and potential often induce only a (relatively) small shift from the exchange- only results. For the ACFD, however, non self-consistent EXX typically underbinds by a considerable degree resulting in wildly inaccurate results. Thus the addition of correlation leads to very large shifts in the exchange-only results, in direct contrast to semilocal correlation. This difference in behavior is directly linked to the non-local nature of the EXX, and even though the exchange-only starting point is often nowhere close to experiment, the non-local correlation from the ACFD corrects this deficiency and yields the missing binding needed to produce accurate results. Thus we find the ACFD approach to be vital in the validation of semilocal results and recommend its use in materials where experimental results cannot be straightforwardly compared to other approximate electronic structure calculations. Utilizing the second-order approximation to Random Phase Approximation renormalized (RPAr) many-body perturbation theory for the interacting density-density response function, we have used a so-called higher-order terms (HOT) approximation for the correlation energy. In combination with the first-order RPAr correction, the HOT method faithfully captures the infinite- order correlation for a given exchange-correlation kernel, yielding errors of the total correlation energy on the order of 1% or less for most systems. For exchange-like kernels, our new method has the further benefit that the coupling-strength integration can be completely eliminated resulting in a modest reduction in computational cost compared to the traditional approach. When the correlation energy is accurately reproduced by the HOT approximation, structural properties and energy differences are also accurately reproduced, as confirmed by finding interlayer binding energies of several periodic solids and compared that to some molecular systems along with some phase transition parameters of SiC. Energy differences involving fragmentation have proved to be challenging for the HOT method, however, due to errors that do not cancel between a composite system and its constituent pieces which has been verified in our work as well. / Physics

Turbulence in the ionosphere is important to understand because it can negatively affect communication signals. This work examines different scenarios in the ionosphere in which turbulence may develop. The two main causes of turbulence considered in this work are the gradient drift instability (GDI) and the Kelvin-Helmholtz instability (KHI). The likelihood of the development of the GDI during the August 17, 2017 total solar eclipse is studied numerically. This analysis uses the ``Sami3 is Also a Model of the Ionosphere" (SAMI3) model to study the effect of the eclipse on the plasma density. The calculated GDI growth rates are small compared to how quickly the eclipse moves over the Earth. Therefore, the GDI is not expected to occur during the solar eclipse. A novel 2D electrostatic pseudo-spectral fluid model is developed to study the growth of these two instabilities and the problem of ionospheric turbulence in general. To focus on the ionospheric turbulence, a set of perturbed governing equations are derived. The model accurately captures the GDI growth rate in different limits; it is also benchmarked to the evolution of instability development in different collisional regimes of a plasma cloud. The newly developed model is used to study if the GDI is the cause of density irregularities observed in subauroral polarization streams (SAPS). Data from Global Positioning System (GPS) scintillations and the Super Dual Auroral Radar Network (SuperDARN) are used to examine the latitudinal density and velocity profiles of SAPS. It is found that the GDI is stabilized by velocity shear and therefore will only generate density irregularities in regions of low velocity shear. Furthermore, the density irregularities cannot extend through regions of large velocity shear. In certain cases, the turbulence cascade power laws match observation and theory. The transition between the KHI and the GDI is studied by understanding the effect of collisions. In low collisionality regimes, the KHI is the dominant instability. In high collisionality regimes, the GDI is the dominant instability. Using nominal ionospheric parameters, a prediction is provided that suggests that there exists an altitude in the upper textit{F} region ionosphere above which the turbulence is dominated by the KHI. / Doctor of Philosophy / In the modern day, all wireless communication signals use electromagnetic waves that propagate through the atmosphere. In the upper atmosphere, there exists a region called the ionosphere, which consists of plasma (a mixture of ions, electrons, and neutral particles). Because ions and electrons are charged particles, they interact with the electromagnetic communication signals. A better understanding of ionospheric turbulence will allow for aid in forecasting space weather as well as improve future communication equipment. Communication signals become distorted as they pass through turbulent regions of the ionosphere, which negatively affects the signal quality at the receiving end. For a tangible example, when Global Positioning System (GPS) signals pass through turbulent regions of the ionosphere, the resulting position estimate becomes worse. This work looks at two specific causes of ionospheric turbulence: the gradient drift instability (GDI) and the Kelvin-Helmholtz instability (KHI). Under the correct background conditions, these instabilities have the ability to generate ionospheric turbulence. To learn more about the GDI and the KHI, a novel simulation model is developed. The model uses a method of splitting the equations such that the focus is on just the development of the turbulence while considering spatially constant realistic background conditions. The model is shown to accurately represent results from previously studied problems in the ionosphere. This model is applied to an ionospheric phenomenon known as subauroral polarization streams (SAPS) to study the development of the GDI and the KHI. SAPS are regions of the ionosphere with large westward velocity that changes with latitude. The shape of the latitudinal velocity profile depends on many other factors in the ionosphere such as the geomagnetic conditions. It is found that for certain profiles, the GDI will form in SAPS with some of these examples matching observational data. At higher altitudes, the model predicts that the KHI will form instead. While the model is applied to just the development of the GDI and the KHI in this work, it is written in a general manner such that other causes of ionospheric turbulence can be easily studied in the future.

Currently, there is a great interest towards developing organic semiconductors for use in solar cells and lighting displays. Derivatives of one of the most important chromophores, diketopyrrolopyrrole (DPP), are commonly employed as the active material in field-effect transistors, as they exhibit high hole mobilities. The intramolecular structure of 2T-DPP-2T with four thiophene units(T) is classified as a donor-acceptor-donor (DAD) chromophore, where the bithiophene units are donors and the DPP unit is the acceptor. The absorption spectrum of the aggregated form of a polymer based on the 2T-DPP-2T repeat units in 1,1,2,2-tetrachloroethane solution (TCE) was measured by Janssen et. al. The spectrum is red-shifted relative to a unaggregated polymer, which is an identifying feature of a J-aggregate. In addition, the ratio of the first two vibronic peaks decreases substantially in going from the unaggregated phase to the aggregate, which is an identifying feature of an H-aggregate. These contradicting behaviors were also observed by Punzi et. al. for an aggregate of the 2T-DPP-2T chromophore. Such behavior cannot be explained by the classical Frenkel-Holstein model. One challenge has been that the intermolecular charge transfer (ICT) plays an important role in the absorption and emission spectrum in the molecular aggregates of DPP. The bulk of this thesis has been to expand the Frenkel-CT-Hosltein model to include intramolecular and intermolecular charge transfer. The model accounts unusual red-shifted H-aggregates observed in the experiments. The experimental spectra of two different DPP-based chromophores are successfully reproduced with our theoretical model. Furthermore, based on perturbative expression for ICT coupling, an effective Frenkel Holstein (EFH) model is proposed and employed to successfully simulate the absorption and emission spectrum of DPP4T aggregates, as long as charge-transfer coupling is smaller than the energy gap between the Frenkel- and ICT excitations. The emission spectrum of DPP4T is also successfully reproduced by this new model, including the temperature dependence. / Chemistry

Title: Modelling of plasma-solid interaction Author: Jan Nožka Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Rudolf Hrach, DrSc., Department of Surface and Plasma Science Abstract: This work is devoted to computer modeling of the low-temperature argon plasma discharge. We created one basic particle model and one basic fluid model. Furthermore, we created a model of electron-electron interaction in three dimensions. This model is able to stabilize nonequilibrium electron gas in the expected equilibrium. This model was developed to investigate the influence of electron-electron scattering on the acceleration of electrons above the speed that is sufficient for excitation or ionization of neutral argon atom. At the end of this work there are results that shed a light on the importance of this interaction in comparison with the amount of fast electrons that are present in the plasma due to electric filed field.

Estudamos transições de fases quânticas em gases bosônicos ultrafrios aprisionados em redes óticas. A física desses sistemas é capturada por um modelo do tipo Bose-Hubbard que, no caso de um sistema sem desordem, em que os átomos têm interação de curto alcance e o tunelamento é apenas entre sítios primeiros vizinhos, prevê a transição de fases quântica superfluido-isolante de Mott (SF-MI) quando a profundidade do potencial da rede ótica é variado. Num primeiro estudo, verificamos como o diagrama de fases dessa transição muda quando passamos de uma rede quadrada para uma hexagonal. Num segundo, investigamos como a desordem modifica essa transição. No estudo com rede hexagonal, apresentamos o diagrama de fases da transição SF-MI e uma estimativa para o ponto crítico do primeiro lobo de Mott. Esses resultados foram obtidos usando o algoritmo de Monte Carlo quântico denominado Worm. Comparamos nossos resultados com os obtidos a partir de uma aproximação de campo médio e com os de um sistema com uma rede ótica quadrada. Ao introduzir desordem no sistema, uma nova fase emerge no diagrama de fases do estado fundamental intermediando a fase superfluida e a isolante de Mott. Essa nova fase é conhecida como vidro de Bose (BG) e a transição de fases quântica SF-BG que ocorre nesse sistema gerou muitas controvérsias desde seus primeiros estudos iniciados no fim dos anos 80. Apesar dos avanços em direção ao entendimento completo desta transição, a caracterização básica das suas propriedades críticas ainda é debatida. O que motivou nosso estudo, foi a publicação de resultados experimentais e numéricos em sistemas tridimensionais [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] que violam a lei de escala $\\phi= u z$, em que $\\phi$ é o expoente da temperatura crítica, $z$ é o expoente crítico dinâmico e $ u$ é o expoente do comprimento de correlação. Abordamos essa controvérsia numericamente fazendo uma análise de escalonamento finito usando o algoritmo Worm nas suas versões quântica e clássica. Nossos resultados demonstram que trabalhos anteriores sobre a dependência da temperatura de transição superfluido-líquido normal com o potencial químico (ou campo magnético, em sistemas de spin), $T_c \\propto (\\mu-\\mu_c)^\\phi$, estavam equivocados na interpretação de um comportamento transiente na aproximação da região crítica genuína. Quando os parâmetros do modelo são modificados de maneira a ampliar a região crítica quântica, simulações com ambos os modelos clássico e quântico revelam que a lei de escala $\\phi= u z$ [com $\\phi=2.7(2)$, $z=3$ e $ u = 0.88(5)$] é válida. Também estimamos o expoente crítico do parâmetro de ordem, encontrando $\\beta=1.5(2)$. / In this thesis, we have studied phase transitions in ultracold atoms trapped in optical lattices. The physics of these systems is captured by Bose-Hubbard-like models, which predicts a quantum phase transition (the so called superfluid-Mott insulator, or SF-MI) when varying the potential depth of the optical lattice in a system without disorder, where atoms have short range interactions, and tunneling is allowed only between nearest neighbors. Our studies followed two directions, one is concerned with the influence of the geometry of the lattice namely, we study the changes in the phase diagram of the SF-MI phase transition when the optical lattice is hexagonal. A second direction is to include disorder in the original system. In our study of the hexagonal lattice, we obtain the phase diagram for the SF-MI transition and give an approximation for the critical point of the first Mott lobe, using a quantum Monte Carlo algorithm called Worm. We also compare our results with the ones from the squared lattice and obtained using mean-field approximation. When disorder is included in the system, a new phase emerge in the ground-state phase diagram intermediating the superfluid and Mott-insulator phases. This new phase is called Bose-glass (BG) and the quantum phase transition SF-BG was the subject of many controversies since its first studies in the late 80s. Though many progress towards its thorough understanding were made, basics characterization of critical proprieties are still under debate. Our study was motivated by the publication of recent experimental and numerical studies in three-dimensional systems [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] reporting strong violations of the key quantum critical relation, $\\phi= u z$, where $\\phi$ is the critical-temperature exponent, $z$ and $ u$ are the dynamic and correlation length critical exponents, respectively. We addressed this controversy numerically performing finite-size scaling analysis using the Worm algorithm, both in its quantum and classical scheme. Our results demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), $T_c \\propto (\\mu-\\mu_c)^\\phi$, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the $\\phi= u z$ law [with $\\phi=2.7(2)$, $z=3$, and $ u = 0.88(5)$] holds true. We also estimate the order parameter exponent, finding $\\beta=1.5(2)$.

Neste trabalho, nossa principal motivação foi o entendimento da dinâmica de pacotes de onda em isolantes topológicos 2D. Como excitações de carga se movem nesses materiais? De que maneira essas trajetórias dependem das condições iniciais, e de que forma as condições de contorno influenciam nessa dinâmica? Essas foram algumas das perguntas que guiaram nosso trabalho. Através de simulações computacionais, estudamos o movimento de pacotes de onda gaussianos em poços quânticos de HgTe/CdTe. O comportamento de isolante topológico para essa heteroestrutura foi prevista teoricamente no importante trabalho de Bernevig et al. (Science, vol. 314, no. 5806, 2006) e confirmada experimentalmente por König et al. (Science, vol. 318, no. 5851, 2007). Estudando-se a evolução temporal desse sistema, foi possível observar trajetórias que dependem de forma evidente, não apenas da orientação de spin, mas também da orientação de um pseudo-spin proveniente do modelo BHZ. Em sistemas com condições de contorno periódicas em ambas as dimensões e sem a aplicação de campos externos, foram observadas trajetórias com formato de espiral, acompanhadas por um \"side-jump\" dependente da direção do spin e do pseudo-spin. Em especial, para o caso em que o pseudo-spin está inicialmente orientado na direção-z, as trajetórias espiraladas foram subtituidas por um padrão do tipo \"zitterbewegung\" dependente de um potencial de \"bias\". Para sistemas confinados com bordas impenetráveis, observou-se a formação de estados de borda helicais característicos de isolantes topológicos. / In this work, our main motivation was the understanding about the dynamics of wave packets in 2D topological insulators. How charge excitations move throughout theses materials? In what way their trajectories depend on the initial conditions, and how boundary conditions change this dynamics? These were some of the questions that have guided us in our work. Using numerical simulations, we have studied the movement of gaussian wave packets in HgTe/CdTe quantum wells. The topological insulator behavior for this heterostructure was theoretically predicted on the important work conducted in 2006 by Bernevig et al. (Science, vol. 314, n. 5806, 2006), and experimentally confirmed by König et al. (Science, vol. 318, no. 5851, 2007) a year later. Studing the time evolution of this system, was possible to observe trajectories that depend evidently, not only from the spin projection, but also from the pseudospin orientation coming from the BHZ model. From simulations with periodic boundary conditions in both of the two dimensions, and without the application of any external fields, we observed spiral trajectories accompanied by a spin and pseudospin dependent side-jump. Especially, for the case in which the pseudospin was iniatially oriented in \"z\" direction, the spiral trajectories were replaced by a pattern of the type \"zitterbewegung\" dependent of a bias potential. For the confined systems with barriers of hardwall type, was observed the formation of helical edge states, that is the fingerprint of topological insulators.