PhD THESES

Asymptotic Hodge Theory in String Compactifications and Integrable Systems

Abstract
String theory is a proposal for a description of nature on the smallest length scales, where both quantum mechanics and gravity are expected to play an essential role. A curious feature of the theory is that its basic building blocks – one-dimensional strings – behave as if they were moving in nine-dimensional space, as opposed to the three-dimensional space we are familiar with. String theory proposes that the six additional dimensions are curled up into extremely small sizes, in a process called “compactification”. Importantly, what happens in these hidden six dimensions has an enormous influence on the physics we observe at larger length scales, including the strength of the interactions between elementary particles and the value of the cosmological constant. An intriguing aspect of string theory is that there are countless possible ways to compactify these extra dimensions, resulting in a vast “landscape” of potential universes, each with distinct physical properties. In a beautiful interplay of physics and mathematics, the physical characteristics of these universes are intricately linked to the geometric properties of the internal six-dimensional space. The main aim of this thesis is to study the latter using the sophisticated mathematical framework of asymptotic Hodge theory. One of the central results is that one can obtain a good approximation of numerous physical observables by studying the allowed singularities of the six-dimensional internal space. In accordance with some fundamental theorems in the field of algebraic geometry, these can be classified in great generality and reveal intriguing underlying structures. In particular, this abstract approach leads to a comprehensive, algorithmic method for calculating physical observables in string compactifications. In this way, we obtain a very general characterization of universes that can be constructed in string theory and find that they are in fact finite in number. Additionally, based on recent advances in the field of tame geometry it is suggested that this number might be much smaller than previously expected. Finally, we observe that the same mathematical structures applied above in the context of string compactifications arise in a completely different corner of physics: the study of integrable non-linear sigma models. In particular, the same computational methods used to compute physical observables in string theory can be used to find previously unknown solutions for certain classes of such models. Our results open up a new avenue of research, bridging two distinct areas of theoretical physics.

Temporal aspects of asymptotic safety:From Euclidean to Lorentzian spacetime

Measurement of D Meson Production. Probing QCD and LFV τ decay with the ATLAS detector

Abstract
The Standard Model, the prevailing theory in particle physics, successfully explains three of the four fundamental forces but has notable limitations. For instance, while it includes neutrinos, it does not account for their observed masses or the force of gravity. Additionally, although it provides accurate predictions, the complexity of calculations required for precise particle production modeling at accelerators can be challenging. This thesis investigates the Ds meson, a particle abundantly produced in accelerators, to study quark production and search for lepton-flavor violations. By analyzing collision data from the ATLAS detector at CERN, the thesis presents differential measurements of Ds meson production, including the previously unexplored high-momentum region. These results are compared to state-of-the-art theoretical predictions to provide valuable feedback to theory. The implications of these findings for improving searches for lepton-flavor-violating tau lepton decays, which are rare processes beyond Standard Model predictions, are also discussed.

Dynamic Ion Transport: From Electrolytic Cells to Conical Channels

Abstract
In this thesis we explore the dynamics of ions in electrolytes under the influence of externally applied time-dependent voltage. The thesis is based on three manuscripts. The first one concerns findings of recent experiments [S. H. Hashemi et al., Physical Review Letters 121, 185504 (2018)], which have shown that a long-ranged steady electric field emerges when applying an oscillating voltage over an electrolyte with unequal mobilities of cations and anions confined between two planar blocking electrodes. To explain this effect we analyse full numerical calculations based on the Poisson-Nernst-Planck equations by means of analytically constructed equivalent electric circuits. Surprisingly, the resulting equivalent circuit has two capacitive elements, rather than one, which introduces a new timescale for electrolyte dynamics. We find a good qualitative agreement between the numerical results and our simple analytic model, which shows that the long-range steady electric field emerges from the different charging rates of cations and anions in the electric double layers. In the second one, building upon the discovery of asymmetric rectified electric fields (AREF) in recent experiments [S.H. Hashemi et al., Physical Review Letters 121, 185504 (2018)], we explore the generation of AREF by applying a sawtooth-like voltage to 1:1 electrolytes with equal diffusion coefficients confined between two planar blocking electrodes. This differs from an earlier approach based on a sinusoidal AC voltage applied to 1:1 electrolytes with unequal diffusion coefficients. By numerically solving the full Poisson-Nernst-Planck equations, we demonstrate that AREF can be generated by a slow rise and a fast drop of the potential (or vice versa), even for electrolytes with equal diffusion coefficients of the cations and anions. We employ an analytically constructed equivalent electric circuit to explain the underlying physical mechanism. Importantly, we find that the strength of AREF can be effectively tuned from zero to its maximal value by only manipulating the time-dependence of the driving voltage, eliminating the necessity to modify the electrolyte composition between experiments. This provides valuable insights to control the manipulation of AREF, which facilitates enhanced applications in diverse electrochemical systems. Finally, in the third one, we study a hitherto unexploited characteristic feature of emerging iontronic devices for information processing – the intrinsic mobility of the medium (water), containing charge carriers (ions), which therefore not only responds to voltage but also to pressure. Here we study a microfluidic memristor, in the form of a conical channel, exposed to simultaneously applied time-dependent voltage and pressure drops, through numerical solutions of the Poisson-Nernst-Planck-Stokes equations for ion and fluid transport. We show that the channel’s memristive properties can be enhanced, reduced or instantaneously reset by a suitable pressure, and we leverage this finding by two examples of time series processing of simultaneously applied voltage and pressure pulses. We not only show that the distinction between different voltage time series can be improved by enhancing the conductance response with corresponding pressure pulses, but also that the bandwidth of information transfer through the channel can be doubled by letting the pressure pulses represent a second independent time series.

Tangent fermions: massless fermions on a lattice

Abstract
In some condensed matter systems, such as the surface of a 3D topological insulator, the electrons are effectively massless and we must necessarily use the massless Dirac equation to describe them.A very convenient way to numerically solve this equation is to discretise them. However, the Nielsen-Ninomiya theorem proves that if we try to do it naively, extra unphysical massless fermion species appear, giving rise to a number of undesired artefacts. This is known as fermion doubling, and the main focus of this thesis is to tackle this problem via the discretisation method of tangent fermions.Chapters 2,3 and 4 are devoted to developing various aspects of this method. Chapters 5 and 6 are not directly related to the method of tangent fermions but still describe processes that arise in materials with a Dirac-like dispersion relation. In chapter 5, we study the effect a non-zero net supercurrent parallel to the edges of a topological superconductor. We find that the supercurrent can induce a “chirality inversion” of the Majorana edge modes.In the last chapter, we simulate the injection of “edge-vortices” into a topological superconductor. These are a type of quasiparticles that can theoretically be used to realise a quantum computer.

Turning through disorder: Models of bundled mucus strands and microswimmers

Abstract
With every breath you take, you can inhale dangerous particles. The respiratory system relies on mucociliary transport (MCT) to clear the airways of such particles. This works as follows: deposited particles are captured by a mucus layer lining the airways, and this mucus layer is propelled out of the lungs by the beating action of ciliated cells that collectively create a flow. Mucus consists of mucins which give the suspension elastic properties. In this thesis, we focus on a specific structure, bundled mucus strands, present in the upper airways of large mammals. These strands are created in submucosal glands and can be millimetric in length. Once they are released from the glands, they come together to form large networks, that catch large particles and drag these out of the airways. We devised minimal models by which we could numerically investigate how bundled strands contribute to MCT. Specifically, we were interested in how such strands reorient from an orientation parallel to the direction of the flow, when they just emerge from the gland, to a perpendicular orientation. We studied the role of surface interactions, involving another mucin structure, and local inhomogeneities in the fluid flow. We found that both can drive reorientation, but that surface interactions best fit the experimental observations. We also considered a simple model for a microswimmer in a (model) viscoelastic environment, to see how the motion of such a particle is affected by its surroundings. In connecting to experiments, we found that local contact dynamics are key in capturing its reorientation.

Classical, quantum and numerical aspects of modified theories of gravity

Abstract
This thesis considers modifications of some specific and well-known gravity theories. In particular, linearised infinite-derivative gravity theories are studied in both four-dimensional and two-dimensional space-time. For the four-dimensional case, some specific quantum aspects of infinite-derivative gravity are examined. This includes an examination of the non-static potential that arises in such a theory when two spinless particles exchange a graviton. Infinite-derivative modifications of two specific two-dimensional gravity theories that have a dilaton field are also constructed in the linearised regime. Non-local modifications to the linearised black-hole solutions of the local theories are then obtained. It is found that the obtained linearised non-local solutions are free of the singular nature that is present in the local case. Finally, a numerical relativity code is constructed to study the evolution of a massless scalar field in the context of the four-dimensional Starobinsky gravity model which is a modification of Einstein’s theory of General Relativity.

The power of one qubit in quantum simulation algorithms

Abstract
This thesis focuses on developing new quantum algorithms, targeting some of the key challenges in the simulation of complex quantum systems.The techniques introduced in this thesis span from quantum state preparation to mitigation of hardware and algorithmic noise, from efficient expectation value measurement to noise-resilient applications in quantum chemistry. 
Quantum computing is an emerging technology, which holds the potential to simulate complex quantum systems beyond the reach of classical numerical methods.Despite recent formidable advancements in quantum hardware, constructing a quantum computer capable of performing useful calculations remains challenging.In the absence of a reliable quantum computer, the study of potential applications relies on mathematical methods, ingenious approximations, and heuristics derived from the fields of application.
A common thread connecting all these algorithms is the introduction of a single auxiliary qubit – a fundamental unit of quantum information – which has an active and distinctive role in the task at hand.

Random Geometry and Quantum Spacetime: From scale-invariant random geometries and asymptotic safety to random hyperbolic surfaces and JT gravity

Abstract
This thesis is driven by a central question: “What can we learn from random geometries about the structure of quantum spacetime?” In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In Chapter 3, we use a construction coming from random geometry called Mating of Trees to build scale-invariant random geometries that appear in Liouville Quantum Gravity and have the potential to implement the UV fixed point predicted by Asymptotic Safety in two and three dimensions. In Chapter 4 we explore the random geometry formulation of JT gravity and how our understanding of random critical maps yields the discovery of a new family of deformations of JT gravity. Furthermore, the connection between JT gravity and matrix models leads us to delve deeper into the link between discrete geometry and hyperbolic surfaces, building upon the geometry of metric maps and irreducible metric maps in Chapter 5.

Studies of generalized transverse momentum dependent gluon distributions in diffractive processes

Abstract
Hadrons, such as protons and neutrons, constitute the dominant components of the visible matter around us. Understanding their internal structures, consisting of quarks and gluons, collectively referred to as partons, requires high energy hadron collisions to probe their contents. At high energies, where hadrons essentially move at high velocities, gluons are predominantly produced, rendering quark contributions negligible. The gluon distributions are described by parton distribution functions (PDFs) dependent on variables related to the parton and hadron momentum. Including more variables in these functions offers a more complete description of the partons. The six dimensional Generalized Transverse Momentum Distribution PDFs (GTMDs), as the counterpart of the Wigner “mother distribution”, provide a comprehensive depiction of parton distribution inside hadrons. We constructed a generic gluon GTMD model based on established models that have successfully described existing data and introduced a few parameters to fit the data. Our model adequately describes diffractive dijet and J/ψ production data, although some tension remains if one aims for a simultaneous description. Future data from experiments on both existing and new accelerators being built can help clarify this tension.