Physics and Astronomy

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This is the collection for the University of Waterloo's Department of Physics and Astronomy.

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A Multi-Phase Analysis of Gas Dynamics and Perturbations in the Galaxy Cluster Cores
(University of Waterloo, 2025-02-14) Li, Muzi
This thesis provides a detailed analysis of gas kinematics and their interactions across various phases within galaxy cluster cores. It examines the processes that generate gas perturbations and the factors that contribute to the thermal stability of the intracluster medium (ICM). A focus is placed on exploring the origins of multi-phase gas and the mechanisms—particularly AGN feedback—that either couple or decouple their motions. Radio-mechanical AGN feedback is identified as one of the most promising heating mechanisms that prevent the cooling of gas. However, the debate on the details of the heating transport processes has remained open. The atmospheres of 5 cool-core clusters, Abell 2029, Abell 2107, Abell 2151, RBS0533 and RBS0540, have short central cooling times but little evidence of cold gas, and jet-inflated bubbles. The amplitudes of gas density fluctuations were measured using a new statistical analysis of X-ray surface brightness fluctuations within the cool cores of these ‘spoil’ clusters in Chapter 2. The derived velocities of gas motions, typically around 100 - 200 km/s, are comparable to those in atmospheres around central galaxies experiencing energetic feedback, such as in the Perseus Cluster, and align well with the turbulent velocities expected in the ICM. Regardless of the mechanisms driving these perturbations, turbulent heating appears sufficient to counteract radiative losses in four of the five spoiler cluster cores. We thus suggest that other mechanisms, such as gas sloshing, may be responsible for generating turbulence, offering a plausible solution to suppress cooling in these structureless atmospheres. Multiphase filaments, key byproducts of AGN feedback, are frequently observed near central galaxies, with their morphologies and kinematics closely linked to bubbles. In Chapter 3, we analyzed the velocity structure functions (VSFs) of warm ionized gas and cold molecular gas, identified through [OII] emission and CO emissions observed by the Keck Cosmic Web Imager (KCWI) and the Atacama Large Millimeter/submillimeter Array (ALMA), respectively, in four clusters: Abell 1835, PKS 0745-191, Abell 262, and RXJ0820.9+0752. Excluding Abell 262, where gas forms a circumnuclear disk, the remaining clusters exhibit VSFs steeper than the Kolmogorov slope. The VSFs of CO and [OII] in RXJ0820 and Abell 262 show close alignment, whereas in PKS 0745 and Abell 1835, were differentiated across most scales, likely due to the churning caused by the radio-AGN. The large-scale consistency in Abell 1835 and RXJ0820, together with scale-dependent velocity amplitudes of the hot atmospheres obtained from Chandra X-ray data, may support the idea of cold gas condensation from the hot atmospheres. X-ray observations have previously been constrained by low energy resolution, which has impeded direct measurements of velocity fields in galaxy clusters. However, the recent release of initial data from the X-ray Imaging and Spectroscopy Mission (XRISM) provides a non-dispersive energy resolution of about 5 eV, facilitating the measurement of line broadening and shifts. In Chapter 4 of this thesis, I detail my contributions to calibrating the optical blocking filters for XRISM using synchrotron beamlines at the Canadian Light Source (CLS) and Advanced Light Source (ALS) prior to its launch, and I discuss the model-based estimation of the parameters of the calibrated filters. This capability for direct measurement of plasma velocities is expected to greatly improve our understanding of the ICM dynamics with high accuracy.
Investigating Abundances in Galaxy Clusters and Gas Motions in M87 using XRISM
(University of Waterloo, 2025-01-24) Dizdar, Neo
Galaxy clusters are the forefront of extragalactic diffuse X-ray astrophysics, yet there are still many questions about their formation and evolution. The creation of XRISM, a new X-ray imaging and spectroscopy mission, will study the metal abundance history of clusters and the conversion of jet energy into atmospheric kinetic energy. XRISM’s payload contains an instrument with the highest spectral resolution (5 eV) in the field of X-ray astronomy so far. With this resolution, we observed metal abundances and the broadening of metal lines through turbulent motions in the intracluster medium. In this thesis I present the conversion of data from the Chandra X-ray Observatory to XRISM’s high-resolution format. This includes the preparation and selection of clusters in Chandra, simulating selected clusters for XRISM and applying for proposals. Finally, we extracted abundance and velocity information from the Virgo cluster’s early XRISM data.
On the Initial Boundary Value Problem in Numerical Relativity
(University of Waterloo, 2025-01-23) Dailey, Conner
The principal goal of this thesis is to properly understand, characterize, and numerically implement initial boundary value problems in numerical relativity. Throughout the history of solving Einstein's field equations on computers, boundaries have been mostly dealt with in an approximate way. For example, boundaries might be placed far away from strongly gravitating sources, where approximations like linearized gravity are valid. It has become necessary however to place boundaries in the strong gravity regime of a dynamical spacetime to model complicated and interesting physics, which necessitates a complete understanding of the initial boundary value problem of Einstein's field equations. One motivation for this comes from a need to simulate black hole echoes. In classical general relativity, black holes are perfectly absorbing objects, where the mass of radially incoming wavepackets of matter or gravitational waves is absorbed by the black hole. Thus conclusive evidence of modifications to general relativity, such as quantum gravity, could include partial reflections of radially incoming wavepackets, called black hole echoes. To properly understand the modifications this would bring to detectable gravitational wave signals, we require simulations where reflecting boundary conditions are imposed close to the horizon of a black hole. Another motivation comes from recent advances in Cauchy characteristic matching, which combines state of the art numerical techniques to obtain physically accurate gravitational waveforms from simulations. This can allow numerical relativists to dramatically save on the computational cost of black hole merger simulations, but only if boundaries can be placed in the strong gravity regime. This thesis presents advances in simulating initial boundary value problems in numerical relativity. Starting with spherical symmetry, a framework for reflecting a scalar field in a fully dynamical spacetime is developed and implemented numerically using the Einstein-Christoffel formulation. The evolution of a wave packet and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole, is studied. Next, this approach is generalized to spacetimes with no symmetries and implemented numerically using the generalized harmonic formulation. The evolution equations are cast into a summation by parts scheme, which seats the numerical method closer to a class of provably numerically stable systems. State of the art numerical methods are demonstrated, including an embedded boundary numerical method that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid. As a demonstration of these frameworks, the evolution of gravitational wave scattering off of a boundary either inside or just outside the horizon of a black hole, is studied. Finally, a boundary condition framework designed to control quasi-local energy flux is proposed motivated by examples from electromagnetism.
The Evolution of Halo Properties Through Binary Major Mergers
(University of Waterloo, 2024-10-17) Marchioni, Justin
Galaxy clusters are massive, gravitationally bound objects composed of a large population of galaxies. Each of these galaxies occupies a dark matter halo and collectively the cluster has its own extended halo. Cluster halos can be described by many structural properties including their mass, concentration, shape, spin, and asymmetry. These properties, among others, can be used as proxies to constrain cosmology. The issue with galaxy clusters is that they are still assembling at the present-day. These clusters primarily grow through mergers, where smaller systems coalesce to form larger ones. If the mass ratio between the two merging components is sufficiently large (i.e. 3:1 or below), this is known as a major merger. The effect of major mergers is to significantly redistribute the matter distribution in the host system. This leads to pronounced fluctuations in the cluster's structural properties during the merger, making measurements of these properties hard to interpret. Therefore, accurately predicting how cluster properties vary during mergers is important in order to use them as a cosmological tool. In this thesis, we use simulations to study how the structure of remnant systems evolves during mergers. These simulations consider the merger of two isolated components, each represented by truncated Navarro-Frenk-White (NFW) profiles. We find that mergers produce oscillations in structural parameters for both the overall remnant and the host system. For example, the host halo's concentration experiences one of two types of responses to the satellite's motion depending primarily on the pericentric passage distance of the orbit. Given the simulation results, we present a semi-analytic model for the evolution of structure in remnant systems due to isolated, binary mergers. The model consists of two components, a treatment for the orbital evolution of the satellite and a prescription for changes in the host halo's potential. This second component is often neglected when modeling satellite orbits in minor mergers. Interestingly, we find that adding a host halo response model has little impact on the orbital evolution of the satellite and its mass loss. In contrast, this model must be incorporated in order to accurately predict how the remnant's structure changes after the satellite first passes pericentre. While our model generally works well at replicating the median concentration for the first two orbits, it is unable to recreate any of the remnant's anisotropy properties (i.e. shape, spin, and asymmetry). Overall, our results provide a framework for analyzing the response of cluster halo properties to mergers in more realistic scenarios.
Characterization and First Results of an Inverse Photoemission Spectrometer
(University of Waterloo, 2024-09-26) Bouliane, Michael
This thesis discusses our efforts to characterize our home built inverse photoemission spectrometer. We review the relevant theoretical and practical considerations for the technique of inverse photoemssion spectroscopy. We then detail our efforts to characterize our low energy electron gun, presenting a method for determining the total current delivered by the beam using just a Faraday cup. Measurements of the beam’s profile are presented and are used to calculate the parallel momentum resolution of the beam. Equally important is the characterization of our photon detectors, which we show are operating in the proportional region with a minimal dark count rate. We ascertained a spectrometer energy resolution of 415(55) meV by performing inverse photoemission measurements on polycrystalline gold foil, single crystal Cu (111), and pyrolytic graphite. As a final demonstration of our spectrometer’s capabilities we provide a full unoccupied band mapping for pyrolytic graphite showing its ability to resolve dispersive electronic features in reciprocal space.
Towards Large Scale Quantum Simulations with Trapped Ions: Programmable XY model, Precise Light Sensing, and Extreme High Vacuum
(University of Waterloo, 2024-09-24) Kotibhaskar, Nikhil
We are currently witnessing a revolution in quantum technologies. Today's controllable quantum devices have reached a complexity that makes it practically intractable to fully simulate their dynamics using current classical supercomputers. Decades of fundamental research and development have led us to this point. In the coming years, billions of dollars in investments from governments and private entities are expected worldwide. Although general-purpose fault-tolerant quantum computers are expected to impact computing profoundly, today's quantum devices are best suited for their analog quantum operation, where a well-controlled quantum simulator mimics the dynamics of the other quantum system being studied. This affords an advantage over classical simulators at the cost of a restricted set of physical phenomena that can be studied. Today's quantum devices are already providing insights into large-scale entanglement, the underlying physics of high-temperature superconductivity, disordered quantum systems, and much more. Enhancing the capabilities of today's analog quantum simulators requires adding more classes of interactions, reducing errors due to calibration and noise, and increasing the system size to allow larger-scale simulations. The work described in this thesis directly addresses these core points for a system of trapped ions, which are ideal quantum simulators of the coupled dynamics of a large number of magnetic spins. First, the theory and experiment pertaining to the simulation of the anisotropic XY model on trapped ions has been presented. The theoretical proposal does not require added technical improvements over what has existed in the field for over a decade. The experimental validation is performed on a system with two 171Yb+ ions. This directly enhances the repertoire of trapped ions simulators and opens avenues to the exploration of high-temperature superconductivity, superfluidity, and spin liquids. The second result is the demonstration of the highest resolution readout of optical intensity and polarization using a single 171Yb+ ion as the field probe. The technique utilized the intensity- and polarization-dependent optical pumping of the ions as a signature to detect light parameters. This will be useful for the characterization of the optical addressing fields in trapped ion quantum simulators and hence for the calibration of large-scale quantum devices. Finally, the design and construction of a large-scale ion trapping apparatus for quantum simulation are described. The ion trap allows for the trapping of more than 50 ions, and the vacuum chamber used to house the trap with pressure below 1.5E-12 mbar (measurement limited by pressure gauge saturation) likely sets a record for the lowest pressure achieved on a room-temperature trapped ions system. This increases the useful simulation time of large-scale trapped-ion devices and paves the way for further enhancement of the scale of the simulations performed. Together, these results are another step in advancing the capabilities of today's quantum devices to explore physical phenomena far beyond the capability of classical supercomputers.
Development of the CHORD Galaxy Search Strategy
(University of Waterloo, 2024-09-24) Hopkins, Hans
This thesis presents my contribution to the CHORD galaxies science case. I helped develop an algorithm that can automatically pick out galaxies from CHORD driftscan data. The method used is a matched filter, and it acts on spatial data and spectral data. On the spatial side, it searches for point sources. Because CHORD is a highly redundant interferometer, it suffers from spatial aliasing. I present a program that is able to predict the severity of spatial aliasing. It predicts that integrating over periods of time is required to break the alias degeneracy, and that "dithering" CHORD (rotating it by a couple degrees) further helps in reducing the alias issue. I offer a framework for estimating the probability of spatial alias confusion. On the frequency side, I present a method of running the matched filter quickly. CHORD frequency data undergoes a process called upchannelization, which would distort the shape of a galaxy profile. I show how this can be accounted for without incurring a large time-cost penalty. Lastly, I discuss how a full matched filter program would be put together, and implications that my research has on selecting search parameters for a future CHORD galaxy survey.
Studying Unmodeled Physics from Gravitational Wave Data
(University of Waterloo, 2024-09-24) Dideron, Guillaume
This thesis explores the detection and analysis of unmodeled physics in Gravitational Wave (GW) data. To this end, we develop the SCoRe framework, which uses the Correlated Residual Power Spectrum (CRPS) between pairs of detectors to identify deviations from our Standard Model (SM) of GW. This model includes General Relativity (GR) as the theory describing gravity, binary Black Holes (BHs) and Neutron Star (NS) merging as the sources of GWs, our model of the noise in the detectors, and the template waveform models used for data analysis. The thesis starts with a theoretical overview of GW physics, including an overview of GR, and how it describes the way GWs are generated and how they propagate and interact with matter. We then discuss the practical aspects of GW detection: the modelling of the noise in the detectors and the data analysis techniques used to extract and interpret GW signals. Next, we describe the SCoRe framework in Chapter 2, which is designed to distinguish between noise and deviations from the SM, while also shedding light on the underlying physics of the deviation. We detail its three main components: cross-correlating residual power between detectors, projecting onto physically motivated or agnostic bases, and combining information from multiple events by assuming a dependence of the unmodeled physics on the source parameters. To illustrate the method, we apply the SCoRe framework to toy models in Chapter 3. We demonstrate how the method can recover unmodeled signals without prior assumptions about their form, how to choose the timescale of cross-correlation, and how the method can be used to perform a null test of the SM. In Chapter 4, we then forecast the precision with which the SCoRe method can recover a deviation from the SM from a population of Binary Black Hole (BBH) mergers observed by a network of third-generation GW detectors. As the method leverages the dependence of the deviation from the SM on the source parameters, we investigate the effect the distribution of these parameters has on the method. For a model where the deviation scales with the chirp mass as a decaying power law, we show that the precision of the constraints on the deviation decreases as the power law becomes steeper. This has implications for constraining higher-dimensional operators in Effective Field Theories (EFTs) of gravity: higher dimensional operators correspond to steeper power laws and are, therefore, harder to constrain with the method. Finally, in Chapter 5, we illustrate another approach to testing the SM of GWs, where the GW signal in an alternative theory of gravity is numerically computed. We give an overview of the mathematical challenges and describe a method, the “fixing the equations” method, which aims to reduce pathologies in evolving EFTs of gravity by controlling energy flow to high frequencies.
Path Integral Monte Carlo simulations of solid parahydrogen using many-body interaction potentials
(University of Waterloo, 2024-09-23) Ibrahim, Alexander
We construct ab initio many-body potential energy surfaces (PES) and use them to perform high-accuracy path integral Monte Carlo (PIMC) simulations of solid parahydrogen. We first perform PIMC simulations of solid parahydrogen using the Faruk-Schmidt-Hinde (FSH) potential, an ab initio 1D two-body PES for parahydrogen constructed by the Roy group in 2015. The simulations are successful at reproducing experimental results for the equilibrium density and for the vibrational matrix shift for solid parahydrogen. However, we find that the two-body PES on its own is too energetically repulsive at higher densities, and greatly overestimates the pressure as a function of density. To improve the accuracy of our simulations, we must include higher-order many-body interactions, such as the three-body and four-body interactions. We then construct an isotropic ab initio three-body PES for parahydrogen. The energies are calculated using the coupled cluster method with singles, doubles, and perturbative triples excitations (CCSD(T)). The calculations are performed using an AVTZ atom-centred basis set, with additional (3s3p2d) midbond functions. We use a machine learning method called the reproducing kernel Hilbert space (RKHS) method to construct a PES from the ab initio energies. The three-body PES is attractive at short distances. We perform PIMC simulations of solid parahydrogen using both the two-body FSH potential and the new three-body PES. The inclusion of the three-body PES improves the agreement with experiment at lower densities. However, at higher densities, the attractive interaction of the three-body PES overcorrects for the repulsive wall of the two-body PES, resulting in a severe underestimation of the pressure-density curve. Next, we construct an isotropic ab initio four-body PES for parahydrogen. The energies are calculated using the CCSD(T) method, using an AVDZ atom-centred basis set with additional (3s3p2d) midbond functions. We use a multilayer perceptron (MLP) to construct a PES from the ab initio energies. We find that the four-body PES is repulsive at short distances. We anticipate that the inclusion of the four-body PES alongside the aforementioned two-body and three-body PESs will improve the agreement of the PIMC simulations of solid parahydrogen with experiment to higher densities than previously found.
Spectral, information-theoretic, and perturbative methods for quantum learning and error mitigation
(University of Waterloo, 2024-09-17) Peters, Evan
We present spectral and information-theoretic characterizations of learning tasks involving quantum systems, and develop new perturbative error mitigation techniques for near-term devices. In the first part of this thesis, we explore connections between quantum information and learning theory. We demonstrate theoretically that kernel bandwidth enables quantum kernel methods associated with a high dimensional quantum feature space to generalize. We then characterize quantum machine learning models that generalize despite overfitting their training data, contradicting standard expectations from learning theory. In such learning tasks, the learner may fail due to noise in the input data. So we next consider a setting where the learner has access to correlated auxiliary noise, a resource that contains information about an otherwise unknown noise source corrupting input data. We use classical Shannon theory to relate the strength of these correlations to the classical capacity of a bit flip channel with correlated auxiliary noise, and we extend this analysis to derive the quantum capacity of a quantum bit flip channel given access to an auxiliary system entangled with the environmental source of the noise. Finally, we derive an information-theoretic guarantee for the learnability of data by an optimal learner and, extending this technique to a quantum setting, we introduce and characterize an entanglement manipulation task that generalizes the notion of classical learning. The second part of this thesis introduces techniques for error mitigation on near-term quantum processors and provides guarantees in the perturbative limit. We introduce a technique for mitigating measurement errors using truncated matrix operations. We then propose and characterize a technique that uses the time-reversibility of a quantum circuit to measure the quality of a subset of qubits, and we apply this technique to assign logical circuits to qubits on a physical device in a nearly optimal manner using a simulated annealing optimization algorithm.
Automated Tuning and Optimal Control of Spin Qubits in Quantum Dot Devices
(University of Waterloo, 2024-09-17) Paurevic, Andrija
Silicon quantum dots present a promising foundation for realizing scalable quantum processors, leveraging the advantages of a mature semiconductor industry. Two significant challenges hinder their development: the laborious tuning of these devices and the coherent control of their spin qubits. This thesis presents contributions towards addressing these challenges by harnessing physics-informed machine learning. Tuning these devices involves navigating complex parameter spaces, plagued with variability and fabrication imperfections, to identify optimal operating conditions. This process demands extensive time and resources by a researcher to perform large amounts of data collection and analysis. My work takes steps towards on achieving fully autonomous tuning of these devices, with the automated formation of a single quantum dot. This work involves the application of data analysis and computer vision techniques to extract relevant features from data, guiding the tuning process in real-time. This tool allows single quantum dots to be formed autonomously, freeing researchers to focus on investigating the physics of the device. Progress in multi-dot systems was also made by developing a data segmentation model that successfully identifies and segments charge and dot configurations in charge stability diagram data. This enables rapid data analysis to determine optimal voltage settings for achieving the desired device state. Optimal control is crucial for guiding quantum systems through unitary operations while minimizing decoherence. Using a simulated open quantum system Hamiltonian for spin qubits, I developed a protocol to optimize experimental control signals, allowing for the implementation of unitary gate operations with arbitrary fidelity. The protocol designed experimental pulses for single-qubit rotations and entangling gates in a two-qubit system, achieving fidelities above the error correction threshold. Additionally, it utilizes modern machine learning frameworks, making it scalable to multi-qubit systems. The work presented in this thesis serves as an important foundation for future advancements in our research group.
Practical design and demonstration of algorithms for quantum devices
(University of Waterloo, 2024-09-17) Ray, Annie
The emergence of noisy intermediate-scale quantum (NISQ) devices represents a significant milestone in the journey towards the development of large-scale fault tolerant quantum computers. These devices have not only opened avenues for demonstrating a quantum advantage but have also advanced the practical development of quantum algorithms for solving challenging problems in physics, chemistry, and computer science. Most notably, this progress has necessitated a tailored approach to algorithm development that considers the specific architecture and hardware constraints of these quantum devices in order to effectively use them. However, the most useful instances of problems that we hope to solve with quantum computers require significant hardware improvements over the state-of-the-art, including at least a hundred fold increase in the number of qubits. The transition from intermediate-scale to large-scale quantum computers also presents other formidable challenges, particularly for engineering precise quantum control at scale. This thesis attempts to narrow the gap between intermediate and large-scale devices by proposing methods to mitigate noise effects on NISQ devices and by enhancing standard quantum algorithms to minimize resource overhead. One focus is on error correction strategies capable of managing noise on quantum devices. Specifically, we demonstrate the robustness of the sweep rule (a decoder for topological quantum codes) against measurement errors in quantum codes. Additionally, we experimentally demonstrate the improvement in performance of entangling non-Clifford operations when encoded in the [[8,3,2]] code, strengthening the case for error correction. Furthermore, we improve a well-known technique known as imaginary time evolution to reduce the associated qubit and entangling gate overhead, making it more amenable to implementation on NISQ devices. By exploring these avenues, we aim to strike a balance, leveraging NISQ devices to expand their computational capabilities in the short term while serving as a sandbox for the development of future large-scale fault-tolerant quantum computers.
Analytical and Computational Studies of Quasi-1D Spin Models
(University of Waterloo, 2024-09-16) Chen, Yushao
This thesis explores quasi one-dimensional (quasi-1D) quantum spin systems, specifically focusing on Kitaev ladders, Heisenberg ladders, and Motzkin chains. The research employs a combination of analytical and numerical tools to systematically study the phase diagrams of these low-dimensional spin lattices, developing a standardized pipeline for analyzing future models of interest within the field of quantum physics. At the core of this investigation is the deep interconnection between low-dimensional quantum systems and their corresponding tensor network structures. Utilizing Matrix Product States (MPS) and the Density Matrix Renormalization Group (DMRG) methodologies, the thesis provides detailed insights into the phase behaviors of these quasi-1D systems. This includes examining novel phenomena such as quantum spin liquids, various magnetic orderings, and symmetry-protected topological orders. These findings not only enhance our understanding of quantum physics but also highlight the effectiveness and adaptability of tensor network approaches in tackling complex theoretical problems.
Aspects of Quantum Gravity: From Black Hole Thermodynamics to Holography
(University of Waterloo, 2024-09-16) Yang, Jiayue
Understanding the nature of quantum gravity remains one of the cutting-edge challenges in modern theoretical physics. Despite widespread interest and extensive research, the formulation of a complete theory of quantum gravity remains an unsolved problem. This thesis aims to explore quantum gravity from two primary perspectives: black hole thermodynamics and holography. Black hole chemistry extends black hole thermodynamics by incorporating the cosmological constant, treating the black hole mass as enthalpy rather than energy, and interpreting the cosmological constant and its conjugate variable as pressure and volume, respectively. Holographic complexity investigates the duality between gravitational quantities in the bulk and quantum complexity on the boundary. This includes various proposals such as complexity=volume (CV), complexity=spacetime volume (CV2.0), complexity=action (CA), and complexity=anything proposals. In our exploration of black hole thermodynamics, we investigate phase transitions near quadruple points, where four distinct black hole phases coexist. Utilizing the free-energy landscape technique within the framework of four-dimensional Einstein gravity coupled with nonlinear electrodynamics (NLE), we undertake the first investigation into the dynamics of recently discovered multicriticality in black holes. By treating off-shell Gibbs free energy as a potential and solving the Smoluchowski equation numerically, we capture the evolution of the state probability distributions during black hole phase transitions. Our study reveals how off-shell Gibbs free energy, shaped by ensemble temperatures, influences these transitions and highlights intricate behaviours such as weak and strong oscillations. In our investigation of holography, we analyze the complexity of conformal field theories (CFTs) compactified on a circle with a Wilson line, corresponding to magnetized solitons in four-dimensional and five-dimensional Anti-de Sitter space (AdS). We explore three distinct proposals for holographic complexity. Our study reveals that these proposals exhibit a confinement-deconfinement phase transition driven by variations in the Wilson line, with the complexity of formation acting as the order parameter for this transition. We find that the proposed volume and action complexity functionals obey a scaling relation with the radius of the circle. We show that this scaling law is applicable to a broad family of potential complexity functionals and conjecture that the scaling law applies to the complexity of conformal field theories on a circle in more general circumstances.
Towards Feshbach Resonances in the S-WAVE Channel
(University of Waterloo, 2024-09-12) Del Franco, Paul
Ultracold molecules offer unique opportunities for studying quantum phenomena. This thesis presents work undertaken to repair and optimize an older experimental setup which last studied Feshbach resonances in the p-wave channel for ultracold Sodium-Lithium (NaLi) molecules. The primary focus of this work was on the process of repairing and reconfiguring the molecule machine back to a working state. This involved the repair of the optical systems which provide the laser light at the required frequencies. The characterization of the dual species atomic beam, leading to the replacement of the Sodium (Na) and Lithium (Li) sources. The re-optimization of the Zeeman slower current and light alignment. The alignment, configuration and optimization of the magneto optical trap, along with configuration of the transfer processes to the magnetic trap. Significant effort was dedicated to evaporative cooling, where we reached near quantum degeneracy temperatures for both species. With both ultracold gases, we optimized the transfer into an optical dipole trap where we could sweep a magnetic field to produce Feshbach molecules. Progress was made towards Stimulated Raman Adiabatic Passage (STIRAP) for efficient transfer into the triplet ground-state. Although the final step in the STIRAP process was not completed, the successful detection of Feshbach molecules was achieved. This work provides a solid foundation for future experiments, including the completion of the triplet ground-state molecule formation and enhanced stability which will allow for the exploration of s-wave Feshbach resonances in NaLi + NaLi collision complexes. This thesis contributes to the understanding of ultracold molecular interactions and offers insight into the problems encountered in the process of restoring and optimizing a complex experimental apparatus.
Towards Dipole Blockade Controlled-NOT Gate Using Ultracold Molecules
(University of Waterloo, 2024-09-10) Byres, Megan
Quantum computing is a promising field that aims to achieve large increases in computational speed by taking advantage of the unique properties of quantum physics. There are many proposals for how it can be implemented in the real world, one of these being the use of Rydberg atoms. Rydberg atoms are limited by the instability of the highly excited Rydberg states, resulting in lifetimes measured in the hundreds of microseconds. Molecules can be used to perform quantum gates with a similar method to Rydberg atoms, and their lifetimes can be several orders of magnitude longer than the lifetimes of Rydberg atoms. This thesis builds on a previous work in which the ideal fidelity of this method was calculated by investigating various real world factors and their implications for the feasibility of molecules as a platform for quantum computing. Additionally, it discusses many changes and improvements to the ovens and larger vacuum system designed to perform these experiments.
Novel Techniques for the Calibration of Systematics in Next Generation Galaxy Surveys
(University of Waterloo, 2024-08-29) Nguyen, Alan
Baryon Acoustic Oscillation (BAO) observations offer a robust method for measuring cosmological expansion. However, the BAO signal in a sample of galaxies can be diluted and shifted by interlopers - galaxies that have been assigned the wrong redshifts. Because of the slitless spectroscopic method adopted by the Roman and Euclid space telescopes, the galaxy samples resulting from single line detections will have relatively high fractions of interloper galaxies. Interlopers with a small displacement between true and false redshift have the strongest effect on the measured clustering. In order to model the BAO signal, the fraction of such interlopers and their clustering need to be accurately known. We introduce a new method to self-calibrate these quantities by shifting the contaminated sample towards or away from us along the line of sight by the interloper offset, and measuring the cross-correlations between these shifted samples. The contributions from the different components are shifted in scale in this cross-correlation compared to the auto-correlation of the contaminated sample, enabling the decomposition and extraction of the component terms. We demonstrate the application of the method using numerical simulations and show that an unbiased BAO measurement can be extracted. Unlike previous attempts to model the effects of contaminants, self-calibration allows us to make fewer assumptions about the form of the contaminants such as their bias. We also introduce a new statistical technique to cosmology, called the Leave One-Out Probability Integral Transform (LOO-PIT), as a complementary test to the standard best fit statistic χ2. This technique combines two concepts: LOO-CV (Leave One Out-Cross Validation), and the well known Probability Integral Transform (PIT). LOO-PIT primarily has the advantage of diagnosing the type of modelling failure as well as relaxing the constraint of assuming Gaussian likelihoods in one’s data analysis, paving the way for more general methods. While it is a general method, we apply LOO-PIT to the problem of diagnosing unknown interlopers in galaxy catalogues.
Branes and Relations in Holography
(University of Waterloo, 2024-08-28) Lee, Ji Hoon
In this thesis, we propose and study a holographic relation between the states of certain D-branes in anti-de Sitter space and trace relations in the dual gauge theory.
EFFECT OF TREHALOSE AND LITHIUM IN MOLECULAR MECHANISM OF NEUROPROTECTION IN ALZHEIMER’S DISEASE
(University of Waterloo, 2024-08-23) Xu, Yue
Alzheimer's Disease (AD) is still a challenging issue for humans since its first case was identified by Alois Alzheimer over one hundred years ago. Approximately thirty years ago, the "Amyloid cascade hypothesis" was proposed, which is a milestone that began to reveal the mystery of AD. The aggregation and deposition of endogenous amyloid-beta (A-beta) proteins in brains are known to be one of the main pathogenic factors of AD. One of the pathways to neurodegeneration driven by A-beta proteins involves A-beta damage to neuronal membranes, which may result in neuron impairment and death. On the other hand, A-beta proteins have antimicrobial properties, suggesting they may serve functionally in the brain. This could be one of the reasons to explain the severe side effects seen in clinical anti-A-beta treatment for AD. Instead of focusing on anti-A-beta, I aim to explore a therapeutic strategy that focuses on membrane protection. The goal of my work is to investigate the potential of membrane-targeted agents, trehalose and lithium, to protect lipid membranes against A-beta toxicity. Trehalose, a natural-derived sugar, is explored as a potential treatment for neurodegenerative Parkinson's Disease. Lithium, as a mood stabilizer, is commonly used for treating bipolar disorder. Both of the agents are investigated for neurological disorders and can interact with cellular membranes with distinct mechanisms. In this thesis, I ask whether their interaction with lipid membranes can protect membranes from A-beta-induced damage, thereby lowering A-beta neurotoxicity. Hence, the entire thesis addresses two main questions. 1. How does trehalose/lithium affect membrane properties? 2. Can trehalose/lithium protect membranes from A-beta toxicity? To explore the two questions for trehalose and lithium, respectively, the thesis is divided into two parts: Part 1 - trehalose (Chapters 3-8) and Part 2 - lithium (Chapters 9-11). In Part 1, I used Langmuir-Blodgett (LB) Trough, atomic force microscopy (AFM), and Kelvin probe force Microscopy (KPFM) to explore the influence of trehalose on the mechanical and electrostatic properties of model lipid monolayers composed of DPPC, POPC lipids, and cholesterol. The study found that trehalose can enhance the fluidity and alter the electrostatic properties of lipid monolayers, with modulation by NaCl. To assess whether trehalose can protect lipid membranes from A-beta damage, I utilized black lipid membrane (BLM) electrophysiological techniques to evaluate the quality and permeability of membranes exposed to trehalose and A-beta. Results from BLM experiments demonstrated trehalose alleviates A-beta-induced membrane disruption. Furthermore, I explored the binding of A-beta to lipid membranes in the presence of trehalose solutions by localized surface plasmon resonance (LSPR) spectroscopy and found that trehalose can reduce A-beta binding to lipid membranes. Finally, I confirmed the unique neuroprotection of trehalose in cell studies, where trehalose decreased the cell mortality rate caused by toxic A-beta proteins. Part 2 explored the potential of lithium in mitigating A-beta toxicity on lipid membranes. Similarly, I used LB trough, AFM, and KFPM to compare the influence of LiCl and KCl on lipid membranes. The results demonstrated the distinct contribution of Li+ and K+ on the mechanical and electrostatic properties of DPPC-POPC-Chol lipid monolayers. Li+ has a pronounced effect on reducing the lipid molecular area, increasing monolayer fluidity, and strongly competing with K+ in interacting with lipid monolayers. Lastly, BLM was employed to evaluate the membrane permeability in exposure to A-beta and LiCl. The membrane conductance results obtained by BLM suggested that the modulation of LiCl at the therapeutic level enhances membrane resilience to A-beta-induced damage. This research exposes the modulation of membrane-active trehalose and lithium on lipid membrane properties and their protective role in AD. It contributes to exploring a new therapeutic approach against A-beta toxicity that focuses on membrane protection, which may aid in developing prevention and treatment strategies for AD.
Constraining the quenching mechanisms of galaxy clusters through the evolution of stellar mass functions within GOGREEN and GCLASS
(University of Waterloo, 2024-08-21) Hewitt, Guillaume
We present an analysis of the stellar mass functions (SMFs) of 17 rich galaxy clusters within the GOGREEN and GCLASS surveys in the redshift range of 0.8 < z < 1.5, down to a stellar mass limit of log(M/M⊙) = 9.5. We fit all the data simultaneously with a model that allows the Schechter function parameters of the quiescent and star-forming populations to vary smoothly with radius and redshift. The model also fits for the concentration parameter of each population, and the quenched fraction is modeled as a smooth function of redshift and velocity dispersion. We fit the data in a Bayesian manner, using MCMC. We find no significant dependence of the shape of the star-forming SMF on radius nor redshift, and find it to be consistent with the field. We confirm previous results of a radial dependence on the quenched fraction. We find a moderately significant radial dependence on the α and M* parameters of the quiescent population SMF. The cluster core has a highly elevated quenched fraction, yet the core quiescent SMF is more similar in shape to the quiescent field. The cluster non-core has an moderately elevated quenched fraction, and its quiescent SMF is more similar to the shape of the star-forming field. We explore the contributions of ‘early mass quenching’ and mass-independent ‘environmental quenching’ models in each of these radial regimes. We find the core to be described primarily by early mass quenching, which we interpret as accelerated quenching of massive galaxies in protoclusters, possibly through merger-driven AGN feedback, and the non-core to be described by environmental-quenching, signifying the increase of mass-independent quenching mechanisms that dominate low redshift clusters.

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