**Abstract: **This thesis examines the consequences of non-Archimedean geometry in holography and many-body physics. In this framework real space is replaced by a non-Archimedean field which is almost always a padic field or an algebraic extension of a p-adic field. The corresponding bulk geometry is replaced by a discrete tree…

**Abstract:** Neutral atoms trapped in optical tweezer arrays have emerged as a promising platform for quantum simulation and quantum computation. The dynamic reconfigurability of optical tweezer traps enables a high degree of single atom control and the ability to generate large-scale defect-free atom arrays in many geometries…

In this thesis, we study generalizations of well-known Majorana fermion models, including the SYK model and the Klebanov-Tarnopolsky tensor model. The models are compared at finite and large N, where we find that the models simplify considerably and can even become solvable.

In chapter 2, we study quantum mechanical models in which…

Spin qubits housed in silicon quantum dots are rapidly emerging as a viable quantum computing platform. In recent years, there have been single- and two-qubit gate demonstrations, which showed high fidelities to the extent that implementing quantum error correction codes appears to be within reach. With the already existing industrial…

This dissertation explores various generalizations of global symmetries and ’t Hooft anomalies. Chapter two is based on work with Po-Shen Hsin and Nathan Seiberg [1]. It is dedicated to the study of one-form global symmetries in three and four dimensions. We investigate their physical implications, classify their ’t Hooft anomalies and analyze…

A promising avenue for studying the origin and evolution of the universe is to measure the Cosmic Microwave Background (CMB), the thermal radiation remaining from the Big Bang after billions of years of expansion. Today, this remnant takes the form of an extraordinarily uniform thermal blackbody of ~2.7 K in temperature. Increasingly precise…

Over the last six years, the LIGO and Virgo gravitational wave detectors have revolutionized gravitational wave astronomy by discovering the first compact binary mergers. There is much to learn about how these systems form in nature, and these discoveries have allowed to start characterizing the astrophysical population of binary black holes…

Ultracold atomic gases in optical lattices are an ideal platform for studying quantum many-body physics. The long timescales and isolated nature of these systems makes them particularly suited for exploring the dynamics of nearly closed quantum systems and their relaxation towards thermal equilibrium. In this thesis, we demonstrate the…

Physics defined on real manifolds and equipped with locality has achieved many successes theoretically as well as in describing our universe. Nevertheless, from a mathematical point of view, it is not as privileged. This thesis explores the possibility of non-Archimedean and non-local physics by studying a range of…

Living systems exhibit spatial differentiation at every scale, from the functional compartments within cells to the biogeography of multi-species communities. In this dissertation, we investigate the emergence and consequences of spatial differentiation in two contexts: biomolecular condensates in eukaryotic cells (Chapter 1) and resource…

Real world phenomenon are inherently nonlinear and complex in a way that usually cannot be understood from first principle. Yet intelligence behaviors appear in biological systems, which are shaped by billions years of evolution, to solve natural challenges. Here, we show a form of collective intelligence at microbial level, emerged in a swarm…

In this thesis we study N = 6 superconformal field theories (SCFTs) in three dimensions. Such theories are highly constrained by supersymmetry, allowing many quantities to be computed exactly. Yet though constrained, N = 6 SCFTs still exhibit a rich array of behaviors, and in various regimes can be dual holographically to M-theory on AdS4 ×S7,…

Phases of matter are splendid, and get more complicated from physical systems to biochemical systems. Simple physics principles are proposed to categorise various phases of matter. The phys- ical principles are often exemplified by simple idealised models. When they are applied to more complicated biochemical systems, some generalisations may…

Underground rare-event search is a substantial branch in particle physics, in which particle dark matter (DM) direct detection and neutrinoless double β decay (0νββ) are two major topics. The elusive nature of the signals puts stringent requirements on the detector contamination level. Some particular interactions also require specific…

Long-Range Coupling of Electron Spins In the quest towards harnessing quantum systems to study quantum physical phenomena and eventually build a universal quantum computer, multiple promising platforms have emerged. Vast progress has been made on the circuit quantum electrodynamics (cQED) platform, where superconducting quantum bits (qubits)…

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