@phdthesis{12732, abstract = {Nonergodic systems, whose out-of-equilibrium dynamics fail to thermalize, provide a fascinating research direction both for fundamental reasons and for application in state of the art quantum devices. Going beyond the description of statistical mechanics, ergodicity breaking yields a new paradigm in quantum many-body physics, introducing novel phases of matter with no counterpart at equilibrium. In this Thesis, we address different open questions in the field, focusing on disorder-induced many-body localization (MBL) and on weak ergodicity breaking in kinetically constrained models. In particular, we contribute to the debate about transport in kinetically constrained models, studying the effect of $U(1)$ conservation and inversion-symmetry breaking in a family of quantum East models. Using tensor network techniques, we analyze the dynamics of large MBL systems beyond the limit of exact numerical methods. In this setting, we approach the debated topic of the coexistence of localized and thermal eigenstates separated by energy thresholds known as many-body mobility edges. Inspired by recent experiments, our work further investigates the localization of a small bath induced by the coupling to a large localized chain, the so-called MBL proximity effect. In the first Chapter, we introduce a family of particle-conserving kinetically constrained models, inspired by the quantum East model. The system we study features strong inversion-symmetry breaking, due to the nature of the correlated hopping. We show that these models host so-called quantum Hilbert space fragmentation, consisting of disconnected subsectors in an entangled basis, and further provide an analytical description of this phenomenon. We further probe its effect on dynamics of simple product states, showing revivals in fidelity and local observalbes. The study of dynamics within the largest subsector reveals an anomalous transient superdiffusive behavior crossing over to slow logarithmic dynamics at later times. This work suggests that particle conserving constrained models with inversion-symmetry breaking realize new universality classes of dynamics and invite their further theoretical and experimental studies. Next, we use kinetic constraints and disorder to design a model with many-body mobility edges in particle density. This feature allows to study the dynamics of localized and thermal states in large systems beyond the limitations of previous studies. The time-evolution shows typical signatures of localization at small densities, replaced by thermal behavior at larger densities. Our results provide evidence in favor of the stability of many-body mobility edges, which was recently challenged by a theoretical argument. To support our findings, we probe the mechanism proposed as a cause of delocalization in many-body localized systems with mobility edges suggesting its ineffectiveness in the model studied. In the last Chapter of this Thesis, we address the topic of many-body localization proximity effect. We study a model inspired by recent experiments, featuring Anderson localized coupled to a small bath of free hard-core bosons. The interaction among the two particle species results in non-trivial dynamics, which we probe using tensor network techniques. Our simulations show convincing evidence of many-body localization proximity effect when the bath is composed by a single free particle and interactions are strong. We furthter observe an anomalous entanglement dynamics, which we explain through a phenomenological theory. Finally, we extract highly excited eigenstates of large systems, providing supplementary evidence in favor of our findings.}, author = {Brighi, Pietro}, issn = {2663-337X}, pages = {158}, publisher = {Institute of Science and Technology Austria}, title = {{Ergodicity breaking in disordered and kinetically constrained quantum many-body systems}}, doi = {10.15479/at:ista:12732}, year = {2023}, } @phdthesis{13081, abstract = {During development, tissues undergo changes in size and shape to form functional organs. Distinct cellular processes such as cell division and cell rearrangements underlie tissue morphogenesis. Yet how the distinct processes are controlled and coordinated, and how they contribute to morphogenesis is poorly understood. In our study, we addressed these questions using the developing mouse neural tube. This epithelial organ transforms from a flat epithelial sheet to an epithelial tube while increasing in size and undergoing morpho-gen-mediated patterning. The extent and mechanism of neural progenitor rearrangement within the developing mouse neuroepithelium is unknown. To investigate this, we per-formed high resolution lineage tracing analysis to quantify the extent of epithelial rear-rangement at different stages of neural tube development. We quantitatively described the relationship between apical cell size with cell cycle dependent interkinetic nuclear migra-tions (IKNM) and performed high cellular resolution live imaging of the neuroepithelium to study the dynamics of junctional remodeling. Furthermore, developed a vertex model of the neuroepithelium to investigate the quantitative contribution of cell proliferation, cell differentiation and mechanical properties to the epithelial rearrangement dynamics and validated the model predictions through functional experiments. Our analysis revealed that at early developmental stages, the apical cell area kinetics driven by IKNM induce high lev-els of cell rearrangements in a regime of high junctional tension and contractility. After E9.5, there is a sharp decline in the extent of cell rearrangements, suggesting that the epi-thelium transitions from a fluid-like to a solid-like state. We found that this transition is regulated by the growth rate of the tissue, rather than by changes in cell-cell adhesion and contractile forces. Overall, our study provides a quantitative description of the relationship between tissue growth, cell cycle dynamics, epithelia rearrangements and the emergent tissue material properties, and novel insights on how epithelial cell dynamics influences tissue morphogenesis.}, author = {Bocanegra, Laura}, issn = {2663 - 337X}, pages = {93}, publisher = {Institute of Science and Technology Austria}, title = {{Epithelial dynamics during mouse neural tube development}}, doi = {10.15479/at:ista:13081}, year = {2023}, } @phdthesis{13331, abstract = {The extension of extremal combinatorics to the setting of exterior algebra is a work in progress that gained attention recently. In this thesis, we study the combinatorial structure of exterior algebra by introducing a dictionary that translates the notions from the set systems into the framework of exterior algebra. We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms. }, author = {Köse, Seyda}, issn = {2791-4585}, pages = {26}, publisher = {Institute of Science and Technology Austria}, title = {{Exterior algebra and combinatorics}}, doi = {10.15479/at:ista:13331}, year = {2023}, } @phdthesis{14422, abstract = {Animals exhibit a remarkable ability to learn and remember new behaviors, skills, and associations throughout their lifetime. These capabilities are made possible thanks to a variety of changes in the brain throughout adulthood, regrouped under the term "plasticity". Some cells in the brain —neurons— and specifically changes in the connections between neurons, the synapses, were shown to be crucial for the formation, selection, and consolidation of memories from past experiences. These ongoing changes of synapses across time are called synaptic plasticity. Understanding how a myriad of biochemical processes operating at individual synapses can somehow work in concert to give rise to meaningful changes in behavior is a fascinating problem and an active area of research. However, the experimental search for the precise plasticity mechanisms at play in the brain is daunting, as it is difficult to control and observe synapses during learning. Theoretical approaches have thus been the default method to probe the plasticity-behavior connection. Such studies attempt to extract unifying principles across synapses and model all observed synaptic changes using plasticity rules: equations that govern the evolution of synaptic strengths across time in neuronal network models. These rules can use many relevant quantities to determine the magnitude of synaptic changes, such as the precise timings of pre- and postsynaptic action potentials, the recent neuronal activity levels, the state of neighboring synapses, etc. However, analytical studies rely heavily on human intuition and are forced to make simplifying assumptions about plasticity rules. In this thesis, we aim to assist and augment human intuition in this search for plasticity rules. We explore whether a numerical approach could automatically discover the plasticity rules that elicit desired behaviors in large networks of interconnected neurons. This approach is dubbed meta-learning synaptic plasticity: learning plasticity rules which themselves will make neuronal networks learn how to solve a desired task. We first write all the potential plasticity mechanisms to consider using a single expression with adjustable parameters. We then optimize these plasticity parameters using evolutionary strategies or Bayesian inference on tasks known to involve synaptic plasticity, such as familiarity detection and network stabilization. We show that these automated approaches are powerful tools, able to complement established analytical methods. By comprehensively screening plasticity rules at all synapse types in realistic, spiking neuronal network models, we discover entire sets of degenerate plausible plasticity rules that reliably elicit memory-related behaviors. Our approaches allow for more robust experimental predictions, by abstracting out the idiosyncrasies of individual plasticity rules, and provide fresh insights on synaptic plasticity in spiking network models. }, author = {Confavreux, Basile J}, issn = {2663 - 337X}, pages = {148}, publisher = {Institute of Science and Technology Austria}, title = {{Synapseek: Meta-learning synaptic plasticity rules}}, doi = {10.15479/at:ista:14422}, year = {2023}, } @phdthesis{14374, abstract = {Superconductivity has many important applications ranging from levitating trains over qubits to MRI scanners. The phenomenon is successfully modeled by Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory has been studied extensively for systems without boundary. However, little is known in the presence of boundaries. With the help of numerical methods physicists observed that the critical temperature may increase in the presence of a boundary. The goal of this thesis is to understand the influence of boundaries on the critical temperature in BCS theory and to give a first rigorous justification of these observations. On the way, we also study two-body Schrödinger operators on domains with boundaries and prove additional results for superconductors without boundary. BCS theory is based on a non-linear functional, where the minimizer indicates whether the system is superconducting or in the normal, non-superconducting state. By considering the Hessian of the BCS functional at the normal state, one can analyze whether the normal state is possibly a minimum of the BCS functional and estimate the critical temperature. The Hessian turns out to be a linear operator resembling a Schrödinger operator for two interacting particles, but with more complicated kinetic energy. As a first step, we study the two-body Schrödinger operator in the presence of boundaries. For Neumann boundary conditions, we prove that the addition of a boundary can create new eigenvalues, which correspond to the two particles forming a bound state close to the boundary. Second, we need to understand superconductivity in the translation invariant setting. While in three dimensions this has been extensively studied, there is no mathematical literature for the one and two dimensional cases. In dimensions one and two, we compute the weak coupling asymptotics of the critical temperature and the energy gap in the translation invariant setting. We also prove that their ratio is independent of the microscopic details of the model in the weak coupling limit; this property is referred to as universality. In the third part, we study the critical temperature of superconductors in the presence of boundaries. We start by considering the one-dimensional case of a half-line with contact interaction. Then, we generalize the results to generic interactions and half-spaces in one, two and three dimensions. Finally, we compare the critical temperature of a quarter space in two dimensions to the critical temperatures of a half-space and of the full space.}, author = {Roos, Barbara}, issn = {2663 - 337X}, pages = {206}, publisher = {Institute of Science and Technology Austria}, title = {{Boundary superconductivity in BCS theory}}, doi = {10.15479/at:ista:14374}, year = {2023}, }