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As it becomes more and more difficult to miniaturize electronic circuits, the information industry is faced with an existential crisis: soon, it will no longer be possible to significantly expand the computational power of tried-and-trusted electronic technology. It should come as no surprise that both science and industry are frantically searching for a way to avert this impending catastrophe, and are even willing to entertain the notion of abandoning conventional electronics altogether if a more future-proof alternative can be found. One field of research that has this potential is spintronics: the use of intrinsic angular momentum---better known as spin---of electrons to store information. One of the key promises of spintronics is the ability to transport digital information without the need to shuttle around electrons, thereby avoiding the adverse phenomenon of Joule heating. To this end, one may simply perturb the magnetic order of a magnetic material. Doing so generates a spin wave or magnon, in which spin is passed between neighboring electrons while their position remains unchanged. In the subfield of magnonics---the study of magnons---the use of electrically insulating magnetic materials is currently being studied extensively by both experimentalists and theoreticians. In this thesis, I study the theoretical properties of magnons in three different systems involving a magnetic insulator and a heavy metal. In Chapter 4, I investigate whether ferromagnetic magnons can contribute to a phenomenon known as unidirectional spin-Hall magnetoresistance (USMR): a change in magnetoresistence of spintronic systems that occurs when the direction of an electric current is reversed. I predict that such an effect can indeed exist, but will most likely be very small. In Chapter 5, I focus on ballistic transport of magnons in one-dimensional ferromagnetic insulator (FI) chains exhibiting strong aniotropy. The anisotropy causes the magnons to become elliptically polarized, which breaks spin conservation and gives rise to characteristics not seen in systems with circular magnons, one example of which is squeezing: a fundamental asymmetry in quantum noise. The strong anisotropy required to produce significant magnon ellipticity is uncommon in real FIs. In Chapter 6, I therefore extend the work of Chapter 5 to antiferromagnetic spin chains, which bear mathematical semblance to anisotropic ferromagnets, but have ellipticity-producing terms that are intrinsically large. I show that the behavior of these systems depends strongly on the coupling to the antiferromagnet's different sublattices. Although fairly minimal representations of real systems are developed in this work, they nevertheless have large, mostly unexplored parameter spaces, providing ample opportunity for further research in the near future. In the case of magnonic USMR in particular, recent experimental work by Liu et al. [Phys. Rev. Lett., 127:207206, Nov 2021] provides observations that run counter to our model, suggesting an extension of our work is necessary to capture the full phenomenology. On longer terms, a thorough understanding of the behavior of magnons may lead to pure-spintronic devices featuring low dissipation and extremely high operating frequencies. This, in turn, may revitalize advancement of computer hardware after the expected breakdown of Moore's law.

The fundamental question that this thesis tries to contribute to is thus: is it possible to code and compute the meaning of phrases, such as "fluffy dog", in a way that encodes not only logical reasoning, but provides a way to return our (possibly multiple) common understanding(s) of such a phrase? We rely on a compositional approach: the grammar rules act as the "computational rules", and the meanings of the individual words compose with each other following those same rules, in a way that is consistent with the type of meaning that we wish to assign to each word. To use the grammar rules in this way, we rely on Lambek types. In this framework, a common noun is represented by a Lambek type n and an adjective is represented by a type n/n. Following the appropriate type composition rules, we can show that these two types can be mapped to the type n. This means that an adjective applied on a noun gives something that can be used in the same place on a sentence. This is very intuitive: "fluffy dog" could always be used in the place of "dog". The meanings must compose in a way that is homomorphic to the grammar composition. Additionally, it is convenient that these individual meanings have a format that a computer can understand. The choice made here comes from an approach to NLP called "distributional" semantics, that is able to extract vector representations of words by looking at the other words that usually appear next to it: "You shall know a word by the company it keeps". Each Lambek type is assigned a vector space, and so the composition takes place using operations in vector spaces. Then, each word of a certain type is assigned an element of the correct vector space, a vector. The vector space associated with the Lambek type n is N, which means that a word like "dog" is represented by a vector in the noun space. In its turn, the vector space associated with the Lambek type n/n is N⊗N, which describe maps between vectors. The elements of this space can be represented as matrices, and so an adjective such as "fluffy" is also represented by a matrix. The composition of the adjective and the noun, thus, is automatically computed by a computer as the application of the respective matrix to the respective vector, which in turn results in a vector in the space N, consistent with the resulting Lambek type n of grammar composition. This framework can be extend to more complex types and grammar formulations, which can get rather computationally heavy. One possibility to make these calculations more computationally efficient is to resort to quantum computation, by having each vector component as a quantum state and by performing the contractions using a quantum circuit. In this thesis we explore those avenues, with special focus on ambiguities that appear due to different possible readings of the same phrase, as is the case of the scope in "old men and women", or relative clauses in Dutch, where "man die de hond bijt" can translate either to "man that bites the dog" or "man that the dog bites". For these, the different possible contractions represent different readings, and they can exist simultaneously in quantum superposition. In the process, we explore ways of improving cosine similarity calculations using a metric tensor, and we develop a quantum computation algorithm that is capable to speed up the process of finding an answer to an open multiple choice question.

In this thesis we have studied various applications of asymptotic Hodge theory in string compactifications. This mathematical framework captures how physical couplings of the resulting effective theories behave near boundaries in the scalar field space where the internal Calabi-Yau manifold degenerates. Here we conclude by giving a summary of each of the three parts in which this thesis is divided. Part I introduced the techniques from asymptotic Hodge theory we used throughout this thesis. We reviewed the results of the nilpotent orbit theorem of Schmid and the multi-variable sl(2)-orbit theorem of Cattani, Kaplan and Schmid. This discussion was tailored to applications in the study of string compactifications, explaining how to describe important physical couplings such as Kähler potentials and flux superpotentials near boundaries in moduli spaces. The nilpotent orbit approximation yields an asymptotic expansion divided into leading polynomial terms with exponential corrections. In turn, the sl(2)-orbit approximation implements a hierarchy in the large field limit towards this boundary, enabling the use of algebraic structures such as sl(2,R)-triples to describe asymptotic behavior. Part II discussed a geometrical application of asymptotic Hodge theory with the construction of general models for asymptotic periods. To be precise, we studied the (3,0)-form periods of the Calabi-Yau manifold near boundaries in complex structure moduli space. These periods determine for instance the N=2 vector sector of Type IIB compactifications and encode part of the N=1 Kähler potential and flux superpotential in Type IIB orientifolds. Taking the constraints imposed by asymptotic Hodge theory as consistency principles, we developed new methods for constructing these periods. We explicitly carried out our program for all possible one- and two-moduli boundaries and constructed general models for their asymptotic periods. Part III discussed two applications of asymptotic Hodge theory in string compactifications. Chapter 7 focused on bounds put by the Weak Gravity Conjecture, which predicts the existence of states whose charge must larger than or equal to its mass compared to the black hole extremality bound. We studied the charge-to-mass ratios of BPS black holes in four-dimensional N=2 supergravity theories arising from Type IIB Calabi-Yau threefold compactifications. Geometrically these states arise from D3-branes wrapped on certain three-cycles of the internal geometry. We computed the asymptotic charge-to-mass ratios for a particular set of sl(2)-elementary states that couple to the asymptotic graviphoton. In turn, we determined the radii of the ellipsoid that forms the extremality region of electric BPS black holes, thereby giving us precise order one bounds. Chapter 8 studied moduli stabilization in asymptotic regimes in complex structure moduli space. We compared two equivalent sets of extremization conditions: a self-duality for the fluxes or demanding vanishing F-terms. The former is formulated via the Hodge star of the underlying geometry, while the latter are computed via the (D, 0)-form periods. By the nilpotent orbit approximation the self-duality condition (or equivalently the scalar potential) then admits a leading polynomial approximation where all exponential corrections can be consistently dropped. In contrast, the F-terms (or equivalently the superpotential) required us to take metric-essential exponential corrections into account.

The understanding of heavy ion collisions and its quark-gluon plasma formation requires a complicated interplay of rich physics in a wealth of experimental data. In this work we compare for identified particles the transverse momentum dependence of both the yields and the anisotropic flow coefficients for both PbPb and $p$Pb collisions. We do this in a global model fit including a free streaming prehydrodynamic phase with variable velocity $v_\text{fs}$, thereby widening the scope of initial conditions. During the hydrodynamic phase we vary three second order transport coefficients. The free streaming velocity has a preference slightly below the speed of light. In this extended model the bulk viscosity is small and even consistent with zero., Comment: 6 pages, 6 figures, see also the companion paper "A Bayesian analysis of Heavy Ion Collisions with Trajectum" (2010.15134). v2: added Fig 7

Most of the technological devices that we use in our daily life are based on electronics. Electronics is based on the movement of electrons through a (semi)conducting material. But as the electrons move in such materials, they will scatter around leading to a loss of energy that is converted into waste heat. One of the main breakthroughs of the last decades is the development of the transistor. A transistor is a device used to amplify or switch electronic signals. Since its development the scaling of electronic circuits has been leading to fast and steady improvement on their efficiency of operation. These advances led to the development of personal computers, mobile phones, touch screens, etc. In 1965 Gordon Moore predicted that the number of transistors in an integrated circuit (or chip) will double every two years. This is now known as Moore’s law. The predictions of Moore’s law worked for around 50 years but in the last decades it seems that the law is coming to a dead end. As the dimension of chips diminishes and the number of transistors grows, the control of the required electric currents to make them work becomes more difficult due to quantum effects and the above-mentioned waste heat. This brings the urgency of new approaches that do not rely on miniaturization of the devices to improve the efficiency of operation of a chip. Magnon spintronics is a promising solution to this issues. It relies on the interaction between electronic spins in a metal with spins in a magnetic material, in general through interfaces. In a magnetic insulator electrons do not move inside the material, avoiding the generation of waste heat. Nevertheless, it is possible to use both the wavelike perturbations of the magnetic order of the spins, known as magnons, as well as spin currents to encode and ultimately transport information. In this thesis we analyzed diverse aspects of magnon spintronics considering both ferromagnetic insulators and antiferromagnetic materials interfaced with metals. We studied the imprints of different phases of magnonic systems such as the quantum magnon Mott insulating state, as well as the hydrodynamic regime and the presence of viscosity in a magnon fluid. We also discussed how antiferromagnetic systems can be used to generate pure spin currents in response to mechanical deformations, and how to achieve Bose-Einstein condensation of excitons through an antiferromagnetic magnon-mediated interaction.

Large-scale structure formation is arguably one of the most important problems of modern cosmology. The standard treatment is based on a point-particle picture and the corresponding Vlasov equation. Here, we take a field-theoretic approach to this problem and identify how field correlators in curved-space time are related to classical particle distributions in phase-space. We obtain the Vlasov equation in a well-defined limit together with field-theoretic corrections which can be studied in a controlled way. We also take a fresh look at the initial conditions for the cosmic microwave background and large-scale structure formation by presenting a two-field inflationary model in which the inflaton couples bi-quadratically to a light spectator field. The spectator induces a rapid production of entropy which significantly alters the initial conditions for the cosmological evolution at the end of inflation by providing large, stochastically independent momentum fluctuations of the gauge invariant curvature perturbation.

In Weyl semimetals the Fermi velocity associated with the approximately linear dispersion of the low-energy quasiparticles near the band touching point is much smaller than the fundamental speed of sound in vacuum. Consequently their conical spectrum is not bound by Lorentz symmetry and can develop tilts and anisotropies, as has been found in real-life materials such as WTe2. Furthermore, perturbations like disorder and Coulomb interactions can obfuscate and complicate the picture that emerges from the free, fully symmetric Weyl fermion model. Our goal is now to investigate how the interplay of these disturbances impacts the scaling behaviour of observables depending on the Density of States, which nominally vanishes at the free theory nodal point. The pyrochlore lattice is composed of corner-sharing tetrahedra that make it impossible to satisfy all the antiferromagnetic interactions between the Ising-like spins. In such spin ice models lowest energy states obey the spin ice rule, which states that every ground state tetrahedron must have two spins pointing inwards and two spins pointing outwards. This can be interpreted as a divergence-free condition of an effective field, with as many of its field lines leaving the tetrahedron as are entering it. Excitations above this extensively degenerate ground state manifold then obtain an interpretation as pairs of sources and sinks of this field. These monopoles are detectable in for example neutron scattering experiments and influence the low-temperature transport behavior of spin ice materials. We have investigated perturbations to a particular set-up in which two of these pyrochlore lattices interpenetrate and their spins interact, resulting in an effective chemical potential for the monopoles that can stabilize them.

In this thesis we investigate general properties of four- and six-dimensional effective actions with minimal supersymmetry obtained from F-theory by compactification on Calabi-Yau manifolds. More specifically, we analyze the 4d N=1 gauge coupling functions and their one-loop corrections, we show the cancellation of chiral anomalies in four and six dimensions when the F/M-theory duality can be utilized and finally we provide yet another strong piece of evidence for the Swampland Distance Conjecture in the context of string theory, by testing it in the K\"ahler moduli spaces of Calabi-Yau threefolds. Along the way, we perform the reduction of M-theory on a Calabi-Yau fourfold in full generality, study in great detail the behaviour of anomalies under circle compactifications, settle the F-theory lift to six-dimension and provide further evidence for the relationships between the Swampland Distance Conjecture, the emergence proposal and the absence of global symmetry.

This thesis centers around so-called Weyl metals, which are materials that have low-energy excitations that behave as if they were massless Weyl fermions with a definite chirality. Weyl metals can host dissipationless currents when applying external electromagnetic fields, temperature gradients and vorticity. The first part of the thesis therefore focuses on these so-called anomalous transport properties of Weyl metals. We compute the corresponding thermoelectric and magnetovortical response matrices in several different cases and consider in detail what changes when the Weyl cones are tilted. The second part of the thesis centers around interaction effects in Weyl metals. Firstly, we find that the due to the massless character of the Weyl fermions, the anomalous magnetic moment is enhanced significantly as compared to the case of massive electrons. In addition, we show that straining a Weyl metal leads to an interesting type of electron-phonon coupling and compute its influence on the electronic spectral function.

In this work, we study the non-equilibrium dynamics of low-dimensional strongly correlated quantum systems, which in our case are generated by sudden and time-dependent quantum quenches. Such non-equilibrium dynamics are a particularly difficult problem, because the time evolution of the initial many-body quantum state, which is governed by the post-quench Hamiltonian, is highly non-trivial. On top of that, applying an operator to this many-body quantum state in order to calculate its expectation values, typically creates an intricate set of excitations. Throughout the thesis, we furthermore contrast the results that we have obtained using exact numerical methods for two microscopic models, namely the Heisenberg and Fermi-Hubbard chains, with results derived from the Luttinger liquid theory, which, in equilibrium, describes the universal behavior of the two models.In the second part of the thesis, we reduce the dimensionality even further and employ complementary numerical and analytical tools to examine the unusual non-equilibrium behavior of a ring-shaped quantum impurity hosting interacting spin-less fermions.

This thesis explores two windows into fundamental physics: (1) textbf{Cosmic inflation}: By considering inflation as a window to the physics at high energies and to quantum gravity, we study two inflationary models. In one model, we study the quantum corrections for Starobinsky's inflationary model cite{Starobinsky:1980te}, in which we investigate how are cosmological observables affected by quantum effects. Our results show that these observables are significantly affected, but they still agree with observations. We stress that the significant deviations from Starobinsky's inflationary model can be used to study and constrain the quantum loop effects during inflation. The other model is a curvaton model, in which the quantum effects induce a non-minimal coupling to gravity. We find that the non-minimal coupling could use to tune the scalar power spectral index $n_s$ and the power spectrum $P_zeta$. (2) textbf{Emergent gravity}: Statistical laws of black hole suggest that gravity is not fundamental but instead of an emergent phenomenon. One such theory was proposed by Verlinde~cite{Verlinde:2016toy}. In order to test the validity of his theory, we propose two tests of the theory: the perihelion advancement of a planet and the microlensing. We find that Verlinde's theory can be probed by the next generation of experiments.

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access --for the first time-- to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models., 11 pages, 10 figures

In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the $U_q[\widehat{\mathfrak{sl}}(2)]$ invariant six-vertex model and the resulting partial differential equation is studied for particular values of the lattice length., 19 pages. v2: affiliation and references updated, minor changes, accepted for publication in J. Math. Phys

Background One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values. Results We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. Conclusion The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry.

We calculate the bulk viscosity, drag force and jet quenching parameter in Improved Holographic QCD. We find that the bulk viscosity rises near the phase transition but does not exceed the shear viscosity. The drag force shows the effects of asymptotic freedom both as a function of velocity and temperature. It indicates diffusion times of heavy quarks in rough agreement with data. The jet quenching parameter values computed via the light-like Wilson loop are in the lower range suggested by data.

We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s-wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.

The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear Poisson–Boltzmann theory and compared with numerical results from nonlinear Poisson–Boltzmann theory. The excess liquid-liquid interfacial tension with respect to the pure salt-free liquid-liquid interfacial tension is found to decompose into a curvature-independent part due to short-ranged interfacial effects and a curvature-dependent electrostatic contribution. Several curvature-dependent regimes of different scalings of the electrostatic excess interfacial tension are identified. Symmetry relations of the interfacial tension upon swapping droplet and bulk liquid are found to hold in the low-curvature limit, which, e.g., lead to a sign change of the excess Tolman length. For some systems a low-curvature expansion up to the second order turns out to be applicable if and only if the droplet size exceeds the Debye screening length in the droplet, independent of the Debye length in the bulk.