Spatial confinement of electrons and their interactions as well as confinement of the spin dimensionality often yield drastic changes of the electronic and magnetic properties of solids. Novel quantum transport and optical phenomena, involving electronic spin degrees of freedom in semiconductor heterostructures, as well as a rich variety of exotic quantum ground states and magnetic excitations in complex transition metal oxides that arise upon such confinements, belong therefore to topical problems of contemporary condensed matter physics. In this work electron spin systems in reduced dimensions are studied with Electron Spin Resonance (ESR) spectroscopy, a method which can provide important information on the energy spectrum of the spin states, spin dynamics, and magnetic correlations. The studied systems include quasi onedimensional spin chain materials based on transition metals Cu and Ni. Another class of materials are semiconductor heterostructures made of Si and Ge. Part I deals with the theoretical background of ESR and the description of the experimental ESR setups used which have been optimized for the purposes of the present work. In particular, the development and implementation of axial and transverse cylindrical resonant cavities for high-field highfrequency ESR experiments is discussed. The high quality factors of these cavities allow for sensitive measurements on μm-sized samples. They are used for the investigations on the spin-chain materials. The implementation and characterization of a setup for electrical detected magnetic resonance is presented. In Part II ESR studies and complementary results of other experimental techniques on two spin chain materials are presented. The Cu-based material Linarite is investigated in the paramagnetic regime above T > 2.8 K. This natural crystal constitutes a highly frustrated spin 1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearestneighbor interactions. The ESR data reveals that the significant magnetic anisotropy is due to anisotropy of the g-factor. Quantitative analysis of the critical broadening of the linewidth suggest appreciable interchain and interlayer spin correlations well above the ordering temperature. The Ni-based system is an organic-anorganic hybrid material where the Ni2+ ions possessing the integer spin S = 1 are magnetically coupled along one spatial direction. Indeed, the ESR study reveals an isotropic spin-1 Heisenberg chain in this system which unlike the Cu half integer spin-1/2 chain is expected to possess a qualitatively different non-magnetic singlet ground state separated from an excited magnetic state by a so-called Haldane gap. Surprisingly, in contrast to the expected Haldane behavior a competition between a magnetically ordered ground state and a potentially gapped state is revealed. In Part III investigations on SiGe/Si quantum dot structures are presented. The ESR investigations reveal narrowlines close to the free electron g-factor associated with electrons on the quantum dots. Their dephasing and relaxation times are determined. Manipulations with sub-bandgap light allow to change the relative population between the observed states. On the basis of extensive characterizations, strain, electronic structure and confined states on the Si-based structures are modeled with the program nextnano3. A qualitative model, explaining the energy spectrum of the spin states is proposed.:Abstract i Contents iii List of Figures vi List of Tables viii 1 Preface 1 I Background and Experimental 5 2 Principles of ESR 7 2.1 The Resonance Phenomenon . . . . . . . . . . . . . . . . . . . 7 2.2 ESR Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 The g -factor . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Relaxation Times . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Lineshape Properties . . . . . . . . . . . . . . . . . . . . 13 2.3 Effective Spin Hamiltonian . . . . . . . . . . . . . . . . . . . . . 15 2.4 Spin-Orbit Coupling . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 d-electrons in a Crystal Field . . . . . . . . . . . . . . . . . . . . 17 2.6 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6.1 Dipolar Coupling . . . . . . . . . . . . . . . . . . . . . . 23 2.6.2 Exchange Interaction . . . . . . . . . . . . . . . . . . . . 23 2.6.3 Superexchange . . . . . . . . . . . . . . . . . . . . . . . 24 2.6.4 Symmetric Anisotropic Exchange . . . . . . . . . . . . 25 2.6.5 Antisymmetric Anisotropic Exchange . . . . . . . . . . 25 2.6.6 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . 26 3 Experimental 27 3.1 Setup for Experiments at 10GHz . . . . . . . . . . . . . . . . . 27 3.2 Implementation of an EDMR Setup . . . . . . . . . . . . . . . . 29 3.2.1 Basic Characterization . . . . . . . . . . . . . . . . . . . 31 3.3 High Frequency Setup . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1 MillimeterWave Vector Network Analyzer . . . . . . . 33 3.3.2 Waveguides and Cryostats . . . . . . . . . . . . . . . . . 34 3.4 Development of the Resonant Cavity Setup . . . . . . . . . . . 35 3.4.1 Mode Propagation . . . . . . . . . . . . . . . . . . . . . 38 3.4.2 Resonant CavityModes . . . . . . . . . . . . . . . . . . 40 3.4.3 Resonant Cavity Design . . . . . . . . . . . . . . . . . . 41 3.4.4 Resonant Cavity Sample Stick . . . . . . . . . . . . . . . 45 3.4.5 Experimental Characterization . . . . . . . . . . . . . . 47 3.4.6 Performing an ESR Experiment . . . . . . . . . . . . . . 53 II Quasi One-Dimensional Spin-Chains 57 4 Motivation 59 5 Quasi One-Dimensional Systems 61 5.1 Magnetic Order and Excitations . . . . . . . . . . . . . . . . . . 63 5.2 Competing Interactions . . . . . . . . . . . . . . . . . . . . . . . 64 5.3 Haldane Spin Chain . . . . . . . . . . . . . . . . . . . . . . . . . 66 6 Linarite 69 6.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.2 Magnetization and ESR . . . . . . . . . . . . . . . . . . . . . . . 71 6.3 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.4 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . 81 6.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7 The Ni-hybrid NiCl3C6H5CH2CH2NH3 83 7.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.2 Susceptibility andMagnetization . . . . . . . . . . . . . . . . . 85 7.3 ESR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.4 Further Investigations . . . . . . . . . . . . . . . . . . . . . . . . 95 7.5 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . 96 8 Summary 99 III SiGe Nanostructures 101 9 Motivation 103 10 SiGe Semiconductor Nanostructures 107 10.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 10.1.1 Silicon and Germanium . . . . . . . . . . . . . . . . . . 107 10.1.2 Epitaxial Growth of SiGe Heterostructures . . . . . . . 109 10.1.3 Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 10.1.4 Band Deformation . . . . . . . . . . . . . . . . . . . . . 112 10.2 Sample Structure and Characterization . . . . . . . . . . . . . 114 11 Modelling of SiGe/Si Heterostructures 119 11.1 Program Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 120 11.2 Implementation of Si/Ge System . . . . . . . . . . . . . . . . . 121 11.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 11.3.1 Single Quantum Dot . . . . . . . . . . . . . . . . . . . . 123 11.3.2 Multiple Quantum Dots . . . . . . . . . . . . . . . . . . 127 11.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 11.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 12 ESR Experiments on Si/SiGe Quantum Dots 135 12.1 ESR on Si Structures . . . . . . . . . . . . . . . . . . . . . . . . . 135 12.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 137 12.2.1 Samples grown at 600◦C . . . . . . . . . . . . . . . . . . 138 12.2.2 Samples grown at 700◦C . . . . . . . . . . . . . . . . . . 139 12.2.3 T1-Relaxation Time . . . . . . . . . . . . . . . . . . . . . 143 12.2.4 Effect of Illumination . . . . . . . . . . . . . . . . . . . . 145 12.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 12.3.1 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . 149 12.3.2 Assignment of ESR Lines . . . . . . . . . . . . . . . . . . 150 12.3.3 Relaxation Times . . . . . . . . . . . . . . . . . . . . . . 153 12.3.4 Donors in Heterostructures . . . . . . . . . . . . . . . . 153 12.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 13 Summary and Outlook 157 Bibliography 163 Acknowledgements 176

Cette thèse porte sur l’analyse et la génération de mouvements expressifs pour des personnages humains virtuels. Sur la base de résultats d’état de l’art issus de trois domaines de recherche différents (la perception des émotions et du mouvement biologique, la reconnaissance automatique des émotions et l’animation de personnages), une représentation en faible dimension des mouvements a été proposée. Cette représentation est constituée de trajectoires spatio- temporelles des extrémités des chaînes articulées (tête, mains et pieds) et du pelvis. Nous avons soutenu que cette représentation est à la fois appropriée et suffisante pour caractériser le contenu expressif du mouvement humain et pour contrôler la génération de mouvements corporels expressifs. Pour étayer ces affirmations, cette thèse propose : i.) Une nouvelle base de données de mouvements capturés. Cette base de données a été inspirée par la théorie du théâtre physique et contient des exemples de différentes catégories de mouvements (à savoir des mouvements périodiques, des mouvements fonctionnels, des mouvements spontanés et des séquences de mouvements théâtraux), produit avec des états émotionnels distincts (joie, tristesse, détente, stress et neutre) et interprétés par plusieurs acteurs. ii.) Une étude perceptuelle et une approche basée classification automatique conçus pour évaluer qualitativement et quantitativement la quantité d’information liée aux émotions encore véhiculée et codée dans la représentation proposée. Nous avons observé que, bien que de légères différences dans la performance aient été trouvées par rapport à la situation dans laquelle le corps entier a été utilisé, notre représentation conserve la plupart des qualités de mouvements liées à l’expression de l’affect et d’émotions. iii.) Un système de synthèse de mouvement capable : (a) de reconstruire des mouvements du corps entier à partir de la représentation à faible dimension proposée, (b) de produire de nouvelles trajectoires extrémités expressives (incluant la trajectoire du pelvis). Une évaluation quantitative et qualitative des mouvements du corps entier générés montre que ces mouvements sont aussi expressifs que les mouvements enregistrés à partir d’acteurs humains. / This thesis addresses the analysis and generation of expressive movements for virtual human characters. Based on previous results from three different research areas (perception of emotions and biological motion, automatic recognition of affect and computer character animation), a low-dimensional motion representation is proposed. This representation consists of the spatio-temporal trajectories of end-effectors (i.e., head, hands and feet) and pelvis. We have argued that this representation is both suitable and sufficient for characterizing the underlying expressive content in human motion and for controlling the generation of expressive whole-body movements. In order to prove these claims, this thesis proposes: i.) A new motion capture database inspired by physical theater theory. This database contains examples from different motion classes (i.e., periodic movements, functional behaviors, spontaneous motions, and theater-inspired motion sequences) and distinct emotional states (happiness, sadness, relaxedness, stress and neutral) performed by several actors. ii.) A user study and automatic classification framework de- signed to qualitatively and quantitatively assess the amount of emotion-related information conveyed and encoded in the proposed representation. We have observed that although slight differences in performance were found with respect to the cases in which the entire body was used, our proposed representation preserves most of the motion cues salient to the expression of affect and emotions. iii.) A simple motion synthesis system able to capable of: a) reconstructing whole-body movements from the proposed low-dimensional representation, and b) producing novel end- effector (and pelvis) expressive trajectories. A quantitative and qualitative evaluation of the generated whole body motions shows that these motions are as expressive as the movements recorded from human actors

The interaction between thermal convection and magnetic field is of interest in geophysical and astrophysical problems as well as in metallurgical processes such as casting or crystallization. A magnetic field may act in such a way to damp the convective velocity field in the melt or to reorganize the flow aligned with the magnetic field. This ability to manipulate the flow field is of technological importance in industrial processes. In this work, a direct numerical simulation of three-dimensional Boussinesq convection in a horizontal layer of electrically conducting fluid confined between two perfectly conducting horizontal plates heated from below in a gravitational and magnetic field is performed using a spectral element method. Periodic boundary conditions are assumed in the horizontal directions. The numerical model is then used to study the effects of imposing magnetic field. Finally, a low dimensional representation scheme is presented based on the Karhunen-Loeve approach.

The field of low-dimensional quantum magnets has received lot of attention owing to the possibility of studying phenomena associated with the quantum nature of matter. Many materials that realize low-dimensional spin arrangements in their structure have been synthesized in the past twenty years due to the emergence and development of crystal growth techniques. These materials have been studied using various experiments in order to explore the wide range of interesting properties predicted theoretically for low-dimensional systems. In this pursuit, novel properties have been observed and many open questions have been raised. One such property that is typically observed in many low-dimensional quantum magnets is heat transport via magnetic excitations. Large magnitudes of magnetic heat conductivity has been found experimentally in materials belonging to this class in addition to the conventionally known phononic heat conduction, and interesting theoretical predictions like the divergence of heat conductivity in certain spin models exist, that have stimulated research in this field. This experimental work mainly deals with the crystal growth and heat transport properties of low-dimensional quantum magnets that include one-dimensional (1D) spin chain systems Sr$_2$CuO$_3$ and SrCuO$_2$, two-dimensional (2D) Heisenberg antiferromagnet La$_2$CuO$_4$, and a five-leg spin ladder La$_8$Cu$_7$O$_{19}$, with a view to understand propagating low-energy magnetic excitations and their interaction amongst themselves, other quasiparticles and impurities present in the systems. These interactions result in scattering processes that govern the magnitude and temperature dependence of heat conductivity. In spite of considerable theoretical and experimental work in the field of heat transport, a complete understanding of the scattering mechanisms is lacking. The work tries to add to the experimental knowledge about magnetic heat transport in such systems and presents cases which motivate the need for theoretical understanding of aspects of heat transport. The focus of this work was twofold. One part focusses on the single crystal growth using the travelling-solvent floating zone (TFSZ) method of materials which realize low-dimensional spin systems in their structure. The TFSZ method is indispensable for growing large single crystals of extraordinary purity, which can be used for investigations using neutrons and other techniques like heat conductivity measurements that probe anisotropic properties. The other part deals with the experimental results on heat transport and other thermodynamic properties of these materials. In order to study the behaviour of the magnetic heat conductivity at high temperatures, and the effect of small amount of magnetic and non-magnetic impurities on the heat transport of 2D Heisenberg antiferromagnet La$_2$CuO$_4$, single crystals of pure La$_2$CuO$_4$, and Ni- and Zn-doped versions, La$_2$Cu$_x$Ni$_{1-x}$O$_4$ and La$_2$Cu$_x$Zn$_{1-x}$O$_4$ for $x$ = 0.001 and 0.003, were grown using the TFSZ method. Heat transport in the pure compound was experimentally investigated for the first time up to very high temperatures of 813 K using two methods, namely the steady state method for low temperatures and the dynamic flash method for measuring high temperature conductivity. Analysis of the magnon mean-free path using empirical models based on semi-classical theories, and qualitative comparison to theoretical calculations seems to suggest that scattering between magnons might play an important role in addition to scattering of magnons with phonons and defects, and that the spin-spin correlation length could be crucial in limiting the mean free path of magnons at high temperatures. These experimental results and indications of probable scattering mechanisms based on non-rigorous analyses and comparisons, strongly motivate the need for theoretical studies. Heat conductivity measurements on the Ni- and Zn- doped versions of La$_2$CuO$_4$ are still incomplete and inconclusive, and hence have not been reported in this work. Heat transport experiments on Ni- and Ca-doped Sr$_2$CuO$_3$ were performed, with a motivation to investigate the role of disorder induced by impurities lying within the spin chains (Ni) and those lying outside the spin chains (Ca), on the heat transport in this system. In both the cases, the magnetic heat transport is observed to be strongly suppressed upon doping. Empirical analysis of the data seems to suggest that in the temperature regime of 100-300 K, the temperature dependence of the mean-free path of magnetic excitations for the Ni- and Ca-doped samples can be described by scattering with defects (Ni and Ca impurities) and phonons alone. However, surprisingly, a strong increase of phononic conductivity is observed perpendicular and parallel to the spin chains of the Ni-doped compounds compared to the pure compounds, whose explanation seems to lie in the existence of an additional dissipative scattering mechanism present in the pure compounds that is lifted upon doping, possibly due to the presence of a spin gap in the doped compounds. The effect of Ni on the Sr$_2$CuO$_3$ and SrCuO$_2$ was also investigated by studying the low energy regime of the spin excitation spectrum using other microscopic probes like nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS). Large single crystals of SrCu$_x$Ni$_{1-x}$O$_2$, with $x$ = 0.01 were grown and used in these experiments that observed the presence of a spin gap in the Ni-doped sample. Further theoretical investigations are however required to understand the possible role of the spin gap in influencing the spin-phonon scattering mechanism, and its relevance to the observed enhancement in phononic conduction. Although we observe that in the case of both 1D and 2D systems, a semi-classical kinetic model for heat transport along with empirical models of scattering processes describe the temperature dependence of the measured heat conductivity surprisingly well in the temperature regime up to 300 K and 800 K respectively, interpretations based on these analyses must be treated as only preliminary, and as a step towards understanding microscopically the scattering mechanisms involved in low-dimensional systems such as the ones discussed in this work. In the direction of exploratory research towards synthesis of novel low-dimensional materials, two cuprate compounds were synthesized in the form of single crystals using the floating zone method for the first time, namely, a five leg $S=tfrac{1}{2}$ antiferromagnetic spin ladder compound La$_8$Cu$_7$O$_{19}$ and an insulating delafossite LaCuO$_{2}$. A bulk 3D antiferromagnetic ordering is observed in La$_8$Cu$_7$O$_{19}$. Heat conductivity of La$_8$Cu$_7$O$_{19}$ is observed to be purely phononic and no contribution from magnetic excitations seem to exist, although the measurements indicates that there is a large anisotropy in heat transport. However, detailed diffraction experiments using x-rays and neutrons indicate that both the crystal and magnetic structures are complicated, and that the details of the structure prevent La$_8$Cu$_7$O$_{19}$ from being a perfect realization of a five-leg spin ladder.

The research in low-dimensional (low-D) quantum spin systems has become an arduous challenge for the condensed matter physics community during the last years. In systems with low dimensional magnetic interactions the exchange coupling is restricted to dimensions lower than the full three-D exhibited by the bulk real material. The remarkable interest in this field is fueled by a continuous stream of striking discoveries like superconductivity, quantum liquid and spin gap states, chiral phases, etc, derived from the strong effect of quantum fluctuations on the macroscopic properties of the system and the competition between electronic and magnetic degrees of freedom. The main goal of the current studies is to reach a broad understanding of the mechanisms that participate in the formation of those novel ground states as well as the characteristic dependence with respect to relevant physical parameters. In this thesis we present the results of an Electron Spin Resonance (ESR)-based study on different quasi-1D spin systems, exemplifying the realization of 1D-magnetic spin-chains typically containing transition metal oxides such as Cu2+ or V4+. The local sensitivity of the ESR technique has been considered useful in exploring magnetic excitation energies, dominant mechanisms of exchange interactions, spin fluctuations and the dimensionality of the electron spin system, among others. Aside from ESR other experimental results, e.g., magnetization and nuclear magnetic resonance besides some theoretical approaches were especially helpful in achieving a proper understanding and modeling of those low-D spin systems. This thesis is organized into two parts: The first three chapters are devoted to the basic knowledge of the subject. The first chapter is about magnetic exchange interactions between spin moments and the effect of the crystal field potential and the external magnetic field. The second chapter is a short introduction on exchange interactions in a 1D-spin chain, and the third chapter is devoted to ESR basics and the elucidation of dynamic magnetic properties from the absorption spectrum parameters. The second part deals with the experimental results. In the fourth chapter we start with the magnetization results from the zero-dimensional endohedral fullerene Dy3N@C80. This system is seemingly ESR “silent” at the frequency of X-band experiments. The fifth chapter shows an unexpected temperature dependence of the anisotropy in the homometallic ferrimagnet Na2Cu5Si4O14 containing alternating dimer-trimer units in the zig-zag Cu-O chains. In the sixth chapter different magnetic species in the layer structure of vanadium oxide nanotubes (VOx-NT) have been identified, confirming earlier magnetization measurements. Moreover the superparamagnetic-like nature of the Li-doped VOx-NT samples was found to justify its ferromagnetic character at particular Li concentration on the room temperature scale. In the seventh chapter the Li2ZrCuO4 system is presented as a unique model to study the influence of additional interactions on frustrated magnetism. The eighth chapter highlights the magnetic properties of the pyrocompound Cu2As2O7. The results suggest significant spin fluctuations below TN. The thesis closes with the summary and the list of references.

In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using eld theoretic techniques like bosonization and renormalization group. This involves the study of currents in Luttinger liquids, and the fate of a persistent current in a 1D system. In the second part of the thesis, we study the different types of Majorana edge modes in a 1D p-wave topological superconductor. Further we extend our analysis to the e ect of an additional s-wave pairing and a Zeeman field on the topological properties, and present a detailed phase diagram and symmetry classification for each of the cases. In the third part, we concentrate on the topological phases in two-dimensional systems. More specifically, we study the experimental realization of SU(3) topological phases in optical lattice experiments, which is characterized by the presence of gapless edge modes at the boundaries of the system. We discuss the specific characteristics required by a such a three component Hamiltonian to have a non-zero Chern number, and discuss a schematic lattice model for a possible experimental realization. The thesis is divided into three chapters, as discussed below: In the first chapter, we study the effect of a boost (Fermi sea displaced by a finite momentum) on one dimensional systems of lattice fermions with short-ranged interactions. In the absence of a boost such systems with attractive interactions possess algebraic superconducting order. Motivated by physics in higher dimensions, one might naively expect a boost to weaken and ultimately destroy superconductivity. However, we show that for one dimensional systems the e ect of the boost can be to strengthen the algebraic superconducting order by making correlation functions fall o more slowly with distance. This phenomenon can manifest in interesting ways, for example, a boost can produce a Luther-Emery phase in a system with both charge and spin gaps by engendering the destruction of the former. In the second chapter, we study the type of Majorana modes and the topological phases that can appear in a one-dimensional spinless p-wave superconductor. We have considered two types of p-wave pairing, 4"" = 4## and 4"" = 4##., and show that in both cases two types of Majorana bound states (MBS) with different spatial dependence emerge at the edges: one purely decaying and one damped oscillatory. Even in the presence of a Zeeman term B, this nature of the MBS persists in each case, where the value of chemical potential and magnetic field B decides which type will appear. We present a corresponding phase diagram, indicating the number and type of MBS in the -B space. Further, we identify the possible symmetry classes for the two cases (based on the ten-fold classification), and also in the presence of perturbations like a s-wave pairing and various terms involving magnetic field. It is seen that in the presence of a s-wave perturbation, the MBS will now have only one particular nature, the damped oscillating behaviour, unlike that for the unperturbed p-wave case. In the third chapter, we study SU(3) topological phases in two dimension. It is shown by Barnett et.al that N copies of the Hofstadter model with 2N Abelian ux per plaquette is equivalent to an N-component atom coupled to a homogeneous non-Abelian SU(N) gauge field in a square lattice. Such models have non-zero Chern number and for N = 3, can be written in terms of the SU(3) generators. In our work, we uncover two salient ingredients required to express a general three-component lattice Hamiltonian in a SU(3) format with non-trivial topological invariant. We nd that all three components must be coupled via a gauge eld, with opposite Bloch phase (in momentum space, if the NN hopping between two components is teik, then for the other two components, this should be te ik) between any two components, and there must be band inversion between all three components in a given eigenstate. For spinless particles, we show that such states can be obtained in a tripartite lattice with three inequivalent lattice sites, in which the Bloch phase associated with the nearest neighbor hopping acts as k-space gauge eld. The second criterion is the hopping amplitude t should have an opposite sign in the diagonal element for one of the two components, which can be introduced via a constant phase ei along the direction of hopping. The third and a more crucial criterion is that there must also be an odd-parity Zeeman-like term (as k ! k, the term changes sign), i.e. sin(k) z term, where z is the third Pauli matrix defined with any two components of the three component basis. In the presence of a constant vector potential, the kinetic energy of the electron gets modified when the vector potential causes a flux to be enclosed. This can generate the desired odd parity Zeeman term, via a site-selective polarization of the vector potential. This can be achieved in principle by suitable modifications of techniques used in Sisyphus cooling, and with a suitable arrangement of polarizer plates, etc. The topological phase is a firmed by edge state calculation, obeying the bulk-boundary correspondence.

Orientador: Eduardo Granado Monteiro da Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-31T21:58:12Z (GMT). No. of bitstreams: 1 Maimone_DamarisTartarotti_M.pdf: 16410863 bytes, checksum: e2b11832e16df32d41492b82c0b5768d (MD5) Previous issue date: 2016 / Resumo: Os antiferromagnetos de baixa dimensionalidade CuSb2O6 e CoSb2O6 foram investigados com espectroscopia Raman polarizada. Foram obtidas informações sobre as propriedades mag- néticas intrigantes e configurações orbitais. Pode-se fazer a atribuição dos modos fonônicos na fase alta simetria tetragonal para ambos compostos. Para o CuSb2O6, uma transição estrutural a TS = 397(3) K manifesta-se através da observação de um novo modo fonônico em ? 670 cm?1 e por uma grande anomalia na frequência do modo em ? 640 cm?1 na fase de baixa simetria monoclínica, evidenciando uma hibridização aumentada das cadeias lineares de Cu-O-O-Cu como resultado de ordenamento orbital dos elétrons 3d do Cu abaixo de TS. Foi observada uma pronunciada forma de linha assimétrica Fano e comportamentos anômalos para a frequência e largura de linha como função da temperatura para o modo A1g em ? 515 cm?1 para o composto CuSb2O6, indicando um forte acoplamento deste modo com excitações eletrônicas (possivelmente orbitais). Finalmente, ambos os compostos apresentam anomalias de frequência na maioria dos fônons abaixo de ? 100 K que foram interpretados em termos de acoplamento spin-fônon, produzindo informações pertinentes sobre as correlações de curto alcance de baixa dimensionalidade spin-spin. Demonstrou-se, portanto, que espectroscopia Raman fonônica é uma ferramenta valiosa para investigar magnetos de baixa-dimensionalidade / Abstract: The low-dimensional antiferromagnets CuSb2O6 and CoSb2O6 were investigated by polarized phonon Raman spectroscopy, providing insights into their intriguing magnetic properties and orbital configurations. An assignment of the observed phonon modes in the high-symmetry tetragonal phase was performed for both compounds. For CuSb2O6, a structural transition at TS = 397(3) K is manifested by the observation of a new phonon mode at ? 670 cm?1 and by a large frequency anomaly of a mode at ? 640 cm?1 in the low-symmetry monoclinic phase, evidencing an enhanced hybridization of the Cu-O-O-Cu linear chains as a result of orbital ordering of Cu 3d electrons below TS. Pronounced asymmetric Fano lineshape and anomalous frequency and linewidth behavior with temperature were observed for the ? 515 cm?1 A1g mode for CuSb2O6, indicating a strong coupling of this mode with electronic (possibly orbital) excitations. Finally, both compounds show frequency anomalies in most phonons below ? 100 K that were interpreted in terms of the spin-phonon coupling, yielding relevant informa- tion on the low-dimensional short-range spin-spin correlations. Phonon Raman spectroscopy is therefore demonstrated to be a valuable tool to investigate low-dimensional magnets / Mestrado / Física / Mestra em Física / 132659/2015-8 / CNPQ

The project covers automatic speech recognition with neural network training using low-dimensional matrix factorization. We are describing time delay neural networks with factorization (TDNN-F) and without it (TDNN) in Pytorch language. We are comparing the implementation between Pytorch and Kaldi toolkit, where we achieve similar results during experiments with various network architectures. The last chapter describes the impact of a low-dimensional matrix factorization on End-to-End speech recognition systems and also a modification of the system with TDNN(-F) networks. Using specific network settings, we were able to achieve better results with systems using factorization. Additionally, we reduced the complexity of training by decreasing network parameters with the use of TDNN(-F) networks.

Tesis por compendio / [EN] The dimensionality of the system plays a decisive role in the behavior of the electronic dynamics of interacting electrons. In particular, the quasi-2D dimensionality is responsible for the unusual behavior observed in graphene-like materials and layered van-der-Waal systems. Moreover, such effects are also observed for superconducting materials of high critical temperature, even in the normal state, due to their low-dimensionality. The experimental study of graphene triggered a growing attention to respective electronic properties, because the honeycomb lattice defines a band structure with two nodal points in the Brillouin zone which determines a relativistic Dirac-type electronic dynamics. Within a theoretical framework, many properties of single-layer graphene have been studied to allow further characterization of this material. These properties are unconventional due to the unique band structure of graphene, which is described in terms of Dirac fermions, creating links with certain theories of particle physics. In fact, several theoretical groups have employed phenomenological models inspired in quantum cromodynamics (i.e. Nambu-Jona Lassino and Gross-Neveu models) applied to the study of graphene properties. These properties are responsible for the unusual phenomena, such as the fractional Hall effect, which allows the possibility for magnetic catalysis of an excitonic gap, ferromagnetism and superconductivity. The research of high critical temperature superconductors with impurity centers is significant for understanding the underlying physics of such disordered systems. While the cuprate family present insulating properties in the pristine state, the undoped iron pnictides (i.e. LaOFeAs) show a semi-metallic behavior. Inspite these diferences, both compounds are layered structures, where the superconducting state is supported by a quasi-2D square lattice. While for iron pnictides this state is formed by the FeAs layer, the cuprate superconducting state is formed by the CuO layer. The current work focuses on the theoretical study of the structural, electronic and optical properties of graphene-type materials, such as bilayer graphene; and also of s- and d-wave superconductors, more specifically iron pnictides and cuprates, respectively. Furthermore, disordered systems will be focused upon since these (quasi-)2D systems are quite sensitive to disorder. Such properties have major importance for technological device applications, as can be observed in the increasing technological fields of high temperature superconductores and electronic devices. The type of perturbations applied to the systems of interest are chemical impurities and/or external electric bias, and these show variations of the electronic and optical properties when compared to the pristine systems. / [ES] La dimensionalidad de un sistema juega un papel fundamental en la conducta de la dinámica de los electrones que interactúan. En particular, la dimensionalidad cuasi-2D es responsable del comportamiento inusual observado en materiales de tipo grafeno y sistemas laminares basados en enlaces de tipo van der Waals. Además, estos efectos también se observan en materiales superconductores de alta temperatura crítica, incluso en el estado normal, debido a su baja dimensionalidad. El estudio experimental del grafeno provocó una atención creciente a sus propie-dades electrónicas, porque su estructura en forma de panal de abejas da lugar a una estructura de bandas con dos puntos nodales en la zona de Brillouin que determina una dinámica electrónica relativista de tipo Dirac. En el plano teórico, muchas propiedades del grafeno de una sola capa se han estudiado para permitir una mayor caracterización de este material. Estas propiedades son poco convencionales debido a la singular estructura de bandas del grafeno, que se describe en términos de fermiones de Dirac, lo que crea vínculos con ciertas teorías de la física de partículas. De hecho, varios grupos teóricos han empleado modelos fenomenológicos inspirados en la cromodinámica cuántica (es decir, los modelos Nambu-Jona Lassino y Gross-Neveu) aplicados al estudio de las propiedades del grafeno. Estas propiedades son responsables de inusuales fenómenos, como el efecto Hall fraccionario, que permite la posibilidad de catálisis magnética de un gap excitónico, ferromagnetismo y superconductividad. La investigación de superconductores de alta temperatura crítica con centros de impurezas es importante para comprender la física subyacente de tales sistemas desordenados. Mientras que la familia de los cupratos presenta propiedades aislantes en estado prístino, los pnictogenuros de hierro sin dopar (es decir, LaOFeAs) muestran un comportamiento semimetálico. A pesar de estas diferencias, ambos compuestos son estructuras en capas, donde el estado superconductor está respaldado por una red cuadrada cuasi-2D. Mientras que para los pnictogenuros de hierro este estado está formado por la capa de FeAs, el estado superconductor de cuprato está formado por la capa de CuO. El presente trabajo se centra en el estudio teórico de las propiedades estructurales, electrónicas y ópticas de los materiales de tipo grafeno, como el grafeno bicapa; y también de superconductores de ondas s y d, más específicamente pnictogenuros y cupratos de hierro, respectivamente. Además, se hace hincapié en sistemas desordenados ya que estos sistemas (cuasi-)2D son bastante sensibles al desorden. Tales propiedades tienen gran importancia para aplicaciones de dispositivos tecnológicos, como se puede observar en la creciente tecnología campos de tensiotrónica y espintrónica. El tipo de perturbaciones aplicadas a los sistemas de interés son las impurezas químicas y campos eléctricos externos. Estas perturbaciones producen variaciones de las propiedades electrónicas y ópticas cuando se comparan con los sistemas prístinos. / [CAT] La dimensionalitat d'un sistema juga un paper fonamental en la conducta de la dinámica dels electrons que interactúen. En particular, la dimensionalitat cuasi-2D és responsable del comportament inusual observat a materials de tipus grafè i sistemes laminars basats en enllaços de tipus van der Waals. A més a més, aquestos efectes també s'observen a materials superconductors d'alta temperatura crítica, inclús al seu estat normal, degut a la seua baixa dimensionalitat. L'estudi experimental del grafè va produir una atenció creixent a les seues propietats electròniques, perque la seua estructura en forma de panal d'abelles dona lloc a una estructura de bandes amb dos punts nodals a la zona de Brillouin que determinen una dinámica electrónica relativista de tipus Dirac. Al planol teòric, moltes propietats del grafè d'una sola capa s'han estudiat per a permetre una major caracterizació d'aquest material. Aquestes propietat són poc convencionals degut a la singular estructura de bandes del grafè, que es descriu mitjançant fermions de Dirac. Aquestos fermions permeten establir víncles amb certes teories de la física de particles. De fet, alguns grups teòrics han empleat models fenomenològics inspirats a la cromodinàmica quàntica (es a dir, els models Nambu-Jona Lassino i Gross-Neveu) aplicats a l'estudi de les propietats del grafè. Aquestes propietats són responsables d'inusuals fenómens, com l'efecte Hall fraccionari, que permet la possibilitat de catálisi magnètica d'un gap excitònic, ferromagnetisme i superconductivitat. La investigació de superconductors d'alta temperatura crítica amb centres d'impureses és important per a comprendre la física subjacent de tals sistemes desordenats. Mentre que la família dels cuprats presenta propietats aïllants en estat pristí, els pnictogenurs de ferro sense dopar (és a dir, LaOFeAs) mostren un comportament semimetálico. Malgrat aquestes diferències, tots dos compostos són estructures en capes, on l'estat superconductor està recolzat per una xarxa quadrada quasi-2D. Mentre que per als pnictogenurs de ferro aquest estat està format per la capa de FeAs, l'estat superconductor dels cuprats està format per la capa de CuO. El present treball es centra en l'estudi teòric de les propietats estructurals, electròniques i òptiques dels materials de tipus grafè, com el grafè bicapa; i també de superconductors d'ones s i d, més específicament pnictogenurs i cuprats de ferro, respectivament. A més a més, es fa emfasi en sistemes desordenats ja que aquestos sistemes (cuasi-)2D són prou sensibles al desordre. Aquestes propietats tenen gran importància per a aplicacions de dispositius tecnològics, com es pot observar a la creixent tecnologia dels camps de la tensiotrònica i l'espintrònica. El tipus de pertorbacions aplicades als sistemes d'interés són les impureses químiques i els camps elèctrics externs. Aquestes pertorbacions produeixen variacions de les propietats electròniques i òptiques quan es comparen amb els sistemes pristins. / César Dos Santos, MJ. (2021). Effects of symmetry breaking in low dimensional materials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176058 / TESIS / Compendio

The present research seeks to advance the understanding and application of Principal Component Analysis (PCA)-based combustion modelling for practical systems application. This work is a consistent extension to the standard PC-transport model, and integrates the use of Gaussian Process Regression (GPR) in order to increase the accuracy and the potential of size reduction offered by PCA. This new model, labelled PC-GPR, is successively applied and validated in a priori and a posteriori studies.In the first part of this dissertation, the PC-GPR model is validated in an a priori study based on steady and unsteady perfectly stirred reactor (PSR) calculations. The model showed its great accuracy in the predictions for methane and propane, using large kinetic mechanisms. In particular, for methane, the use of GPR allowed to model accurately the system with only 2 principal components (PCs) instead of the 34 variables in the original GRI-3.0 kinetic mechanism. For propane, the model was applied to two different mechanisms consisting of 50 species and 162 species respectively. The PC-GPR model was able to achieve a very significant reduction, and the thermo-chemical state-space was accurately predicted using only 2 PCs for both mechanisms.The second part of this work is dedicated to the application of the PC-GPR model in the framework of non-premixed turbulent combustion in a fully three-dimensional Large Eddy Simulation (LES). To this end, an a posteriori validation is performed on the Sandia flames D, E and F. The PC-GPR model showed very good accuracy in the predictions of the three flames when compared with experimental data using only 2 PCs, instead of the 35 species originally present in the GRI 3.0 mechanism. Moreover, the PC-GPR model was also able to handle the extinction and re-ignition phenomena in flames E and F, thanks to the unsteady data in the training manifold. A comparison with the FPV model showed that the combination of the unsteady data set and the best controlling variables for the system defined by PCA provide an alternative to the use of steady flamelets parameterized by user-defined variables and combined with a PDF approach.The last part of this research focuses on the application of the PC-GPR model in a more challenging case, a lifted methane/air flame. Several key features of the model are investigated: the sensitivty to the training data set, the influence of the scaling methods, the issue of data sampling and the potential of a subgrid scale (SGS) closure. In particular, it is shown that the training data set must contain the effects of diffusion in order to accurately predict the different properties of the lifted flame. Moreover, the kernel density weighting method, used to address the issue of non-homogenous data density usually found in numerical data sets, allowed to improve the predictions of the PC-GPR model. Finally, the integration of subgrid scale closure to the PC-GPR model allowed to significantly improve the simulations results using a presumed PDF closure. A qualitative comparison with the FPV model showed that the results provided by the PC-GPR model are overall very comparable to the FPV results, with a reduced numerical cost as PC-GPR requires a 4D lookup table, instead of a 5D in the case of FPV. / Le double défi de l'énergie et du changement climatique mettent en avant lanécessité de développer des nouvelles technologies de combustion, étantdonné que les projections les plus réalistes montrent que la plus grandeaugmentation de l'offre d'énergie pour les décennies à venir se fera à partirde combustibles fossiles. Ceci représente donc une forte motivation pour larecherche sur l'efficacité énergétique et les technologies propres. Parmicelles-ci, la combustion sans flamme est un concept nouvellementdéveloppé qui permet d'obtenir des rendements thermiques élevés avecdes économies de carburant tout en maintenant les émissions polluantes àun niveau très bas. L'intérêt croissant pour cette technologie est égalementmotivé par sa grande flexibilité de carburant, ce qui représente uneprécieuse opportunité pour les carburants à faible valeur calorifique, lesdéchets industriels à haute valeur calorifique et les combustibles à based'hydrogène. Etant donné que cette technologie est plutôt récente, elle estde ce fait encore mal comprise. Les solutions d'une application industriellesont très difficiles à transposer à d'autres. Pour améliorer les connaissancesdans le domaine de la combustion sans flamme, il est nécessaire de menerdes études fondamentales sur ce nouveau procédé de combustion afin defavoriser son développement. En particulier, il y a deux différencesmajeures par rapport aux flammes classiques :d’une part, les niveaux deturbulence rencontrés dans la combustion sans flamme sont rehaussés, enraison des gaz de recirculation, réduisant ainsi les échelles de mélange.D'autre part, les échelles chimiques sont augmentées, en raison de ladilution des réactifs. Par conséquent, les échelles turbulentes et chimiquessont du même ordre de grandeur, ce qui conduit à un couplage très fort.Après un examen approfondi de l'état de l'art sur la modélisation de lacombustion sans flamme, le coeur du projet représentera le développementd'une nouvelle approche pour le traitement de l'interaction turbulence /chimie pour les systèmes sans flamme dans le contexte des simulationsaux grandes échelles (Large Eddy Simulations, LES). Cette approche serafondée sur la méthode PCA (Principal Component Analysis) afin d'identifierles échelles chimiques de premier plan du processus d'oxydation. Cetteprocédure permettra de ne suivre sur la grille LES qu'un nombre réduit descalaires non conservés, ceux contrôlant l'évolution du système. Destechniques de régression non-linéaires seront couplées avec PCA afind’augmenter la précision et la réductibilité du modèle. Après avoir été validégrâce à des données expérimentales de problèmes simplifiés, le modèlesera mis à l'échelle afin de gérer des applications plus grandes, pertinentespour la combustion sans flamme. Les données expérimentales etnumériques seront validées en utilisant des indicateurs de validationappropriés pour évaluer les incertitudes expérimentales et numériques. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished