School of Physics - Theses

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    Massive Black Holes
    Paynter, James Robert ( 2023-08)
    Black holes are one of the most fundamental astrophysical objects in our universe. In this thesis I look at massive black holes (MBH) with masses $10^{4}-10^{10}$ times that of our sun. In particular, I investigate how their gravitational influence distorts photon trajectories and describe how this can be used to study MBH. This phenomena, known as gravitational lensing, results in changes in shape and brightness of the images of the source as seen by a distant observer. The most striking manifestation of gravitational lensing is multiple images, known as \emph{strong} gravitational lensing. Strong gravitational lensing also results in the magnification of one or more of the images above that which would have been observed in the absence of deflecting matter. The number of cosmological black holes (MBH that do not belong to a galaxy core) is not well constrained. Gravitational lens statistics is one of the few ways to probe their number density. The fraction of sources experiencing strong gravitational lensing (multiple-image formation) is proportional to the number density of gravitational lenses which are able to form such images. GRBs are short bursts of $\gamma$-rays which signify the birth of a stellar mass black hole. Gravitational lensing of time-series data (light-curves) manifests as repetition of the primary signal as a lensed ``echo''. I describe the Bayesian parameter estimation and model selection software \pygrb{} which I wrote for this thesis. I use \pygrb{} to analyse GRB lens candidates from the Burst And Transient Source Experiment (BATSE) GRB catalogue to determine how similar the putative GRB lensed echo images are. I find one convincing candidate -- GRB~950830 -- which passes all our tests for statistical self-similarity. I conclude that GRB~950830 was gravitationally lensed by a $(1+z_l)M_l\approx\unit[5.5\times 10^4]{\msun}$ intermediate mass black hole (IMBH). Furthermore, based on the occurrence rate of this lensing event, I am able to estimate that the density of IMBH in the universe is $n_\textsc{imbh}=\unit[6.7^{+14.0}_{-4.8}\times10^{3}]{Mpc^{-3}}$. I also study the merger of black holes, looking at the recoiling quasar E1821+643 (E1821 hereafter). E1821 has a mass of $\mbh \sim \unit[2.6\times10^9]{\msun}$ and is moving with a line-of-sight velocity $v_\text{los}\approx \unit[2,070\pm50]{\kms}$ relative to its host galaxy. I use Bayesian inference to infer that E1821+643 was likely formed from a binary black hole system with masses of $m_1\sim 1.9^{+0.5}_{-0.4}\times \unit[10^9]{M_\odot}$, $m_2\sim 8.1^{+3.9}_{-3.2} \times \unit[10^8]{M_\odot}$ (90\% credible intervals). Given our model, the black holes in this binary were likely to be spinning rapidly with dimensionless spin magnitudes of ${\chi}_1 = 0.87^{+0.11}_{-0.26}$, ${\chi}_2 = 0.77^{+0.19}_{-0.37}$. I find that E1821+643 is likely to be rapidly rotating with dimensionless spin ${\chi} = 0.92\pm0.04$. Recoiling black holes are one method to populate the universe with massive black holes, however, these are expected to be rare. Massive black holes carry with them a tight cluster of stars and stellar remnants. These stars will pass through the optical caustic(s) of the black hole occasionally, which may lead to observable brightening of the star. Magnifications of greater than one million can easily be achieved, which I term ``Gargantuan Magnification Events'' (GMEs). I estimate the rate at which this lensing occurs, including the distribution of magnifications and event durations. I consider GMEs of pulsars in orbit of MBH as a possible generating mechanism for Fast Radio Bursts (FRBs). I find that pulsar GMEs are able to account for $0.1-1\%$ of the total FRB rate as observed by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) radio observatory. These seemingly unrelated problems all tied together in the end. This thesis is a study of black holes, their interaction with light and matter, and how they evolve through cosmic time. Many lifetimes of work have gone into generating the theory behind the sentence just prior. I hope that my contributions embellish these theories.
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    Developing and applying quantum sensors based on optically addressable spin defects
    Healey, Alexander Joseph ( 2023-04)
    Quantum sensing aims to further our understanding of the natural world and support an upcoming technological revolution by exploiting quantum properties or systems to exceed the performance of classical sensing. Owing to their convenient modes of operation and strong room temperature quantum properties, optically active spin defects hosted within solid state materials have come to prominence as one of the foremost tools of choice in this landscape. Many applications now aim to leverage dense ensembles of such defects to boost measurement sensitivity or scale up, which places greater emphasis on the quality of the host material and sensor production methods since cherry-picking individual defects is no longer an option. The prototypical example of such a defect is the nitrogen-vacancy (NV) centre in diamond, which exhibits remarkable room temperature spin coherence, bestowed upon it by diamond's material properties. In this thesis, we first look at optimising the production of NV ensembles for quantum sensing, aiming to efficiently and cost-effectively produce sensors capable of performing high sensitivity measurements in two key regimes that will be central to the experimental applications explored later. The topics examined are hyperpolarisation of a nuclear spin ensemble on the diamond surface through coupling to an ultra-near-surface NV layer, and investigating the properties of a van der Waals antiferromagnet through widefield NV microscopy. The demands placed on the NV layer for these applications are diverse from one another, with charge stability and quantum coherence properties being vital for the former, and the ability to scalably and reproducibly create layers of known thickness crucial to the latter. In light of these studies, we finally consider whether a different spin system housed within an entirely separate materials system, the boron-vacancy defect in hexagonal boron nitride, may be a suitable alternative to the well-established NV diamond system. We find that the distinct properties of the new host material provide both advantages and disadvantages compared to diamond, and that this system could allow quantum sensing to find even broader scope in the future. By investigating the link between host material properties and the suitability of a quantum sensor for given applications, this thesis provides a unique perspective on the future of the field, which will likely demand more highly specialised and varied sensors.
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    Deterministic implantation of donor ions in near-surface nanoarrays for silicon quantum computing
    Robson, Simon Graeme ( 2023-08)
    Remarkable theoretical and experimental progress has been achieved with donor-based silicon quantum computing architectures in the last decade, firmly cementing this implementation as one of the forerunners in the race to build the first large-scale quantum computer. By employing near-surface donor atoms (P, As, Sb, Bi) as the storage medium, both their nuclear and electronic spin states can be used to encode quantum information. Silicon is an excellent host material, having the advantage that donor atoms can easily be incorporated into its lattice, as well as being able to be isotopically enriched into 28Si, giving donor spin coherence times in excess of 30 s. Despite a significant number of experimental challenges, the end goal of creating a near-surface entangled donor array to enable multi-qubit operations is in sight. The aim of this work is to address some significant recent advances towards this goal through the use of directed implantation of single donor ions. Ion implantation has previously been shown to be a valid method for introducing donor-qubits into silicon, and for decades has been a well-established fabrication technique in the classical semiconductor industry. In this work, it is shown that by employing silicon-based active detection substrates connected to an ultra-low noise charge-sensitive preamplifier, single donor ions can be deterministically implanted at depths between 10 - 20 nm with a detection confidence exceeding 99.8%. The recent acquisition of an in-situ stepped nanostencil extends this concept further to allow the controlled placement of single donors to a lateral precision of around 50 nm. Through the use of a step-and-repeat procedure, the ability to form two-dimensional qubit nanoarrays with this system is demonstrated. With the technique readily capable of scaling up to hundreds of qubits or more, this represents a significant milestone towards the realisation of a top-down solid state qubit architecture. A complementary method for single donor placement in silicon is also given, again using ion implantation. It involves the use of a focused ion beam instrument that has been modified to include a keV electron-beam-ion-source to give access to a large selection of ion species, focused to a 180 nm spot size. By integration of the same high-confidence single ion detection technology, it is shown that this technique is also capable of creating large-scale donor arrays in silicon, but without the need for a physical mask. Its use as not just a single ion implanter, but also a novel instrument for near-surface characterisation of semiconductors is also presented. The system's functionality is demonstrated through the identification of fabrication faults in a silicon-based device that otherwise may have gone undetected through conventional characterisation methods. The adaptation of the focused ion beam technique into an efficient method for creating micro-volumes of isotopically pure 28Si is also explored. This is an important area of focus required to achieve ultra-long qubit coherence times, with the results of a preliminary characterisation confirming the technique's suitability. Finally, adapting the single ion detection technology to demonstrate a new approach for performing high-resolution Rutherford backscattering spectrometry is also presented. Some major advantages include a small physical detector footprint and ease of integration into existing beamline structures. In keeping with the overall theme of this study, the system is used to analyse samples pertinent to silicon donor quantum computing, such as shallowly implanted donors and enriched 28Si wafers. The series of experiments performed in this thesis thus represent some significant steps towards achieving the scalable fabrication of a donor-based silicon quantum computer.
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    Towards Automating the Design and Optimisation of Particle Accelerators
    Zhang, Xuanhao ( 2023-06)
    The question of efficiency and optimality of accelerator lattice structures was investigated in this thesis. Within the context of circular accelerators for hadron therapy, an analysis on the design methodology of existing compact circular acceler-ators was carried out. This analysis prompted the design of a novel lattice based on two double bend achromat arcs as an alternative to conventional periodic cell struc-tures. The feasibility to perform slow extraction for hadron therapy purposes was demonstrated using the proposed lattice. The extraction efficiency was optimised by tuning the lattice optics. In the second half of this thesis, an automated design and optimisation algorithm was proposed. This algorithm was developed as a general purpose lattice design tool. The development process examined three optimisation routines including the Simulated Annealing algorithm, a simple genetic algorithm, and the Non-dominated Sorting Genetic Algorithm (NSGA). Three encoding methods were developed to represent the accelerator lattice for use with the optimisation routines. Namely, the finite slicing encoder, the neural network encoder, and the matrix encoder. It was found that the combination of NSGA-III algorithm and the matrix encoder was the most efficient method for exploring the feasible parameter space for a generalisable lattice design problem.
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    Surface acoustic wave neuromodulation
    Peng, Danli ( 2023-03)
    Neurological disorders such as Alzheimer's disease often involve impaired axonal function, underscoring the importance of modulating diffusion processes within axons for treatment. Surface Acoustic Waves (SAWs) offer a promising avenue for this, given their unique properties like miniaturized dimensions, absence of shock waves, and reduced self-heating compared to traditional ultrasound methods. This thesis explores the utility of SAWs in enhancing axonal diffusion as a potential treatment for neurological disorders characterized by axonal dysfunction. The initial phase of the research employed retinal ganglion cells as a model system for studying diffusion. The axons of retinal ganglion cells are naturally radially aligned and serve as a well-established model, offering advantages in data analysis and reducing error. A mathematical model was established to measure dye diffusion in these cells, laying the groundwork for understanding diffusion mechanisms that are broadly applicable, including but not limited to Alzheimer's disease. Subsequently, I investigated the SAW-driven diffusion enhancement in artificial axons, represented by microchannels. My findings indicate up to a 39% increase in diffusion rates within these microchannels when subjected to SAWs. Numerical simulations were conducted to understand the acoustic pressure fields and acoustic streaming fields, elucidating the mechanisms behind SAW-based diffusion enhancement. Lastly, I explored the biological implications of SAWs by studying their effects on astrocyte recovery, a key factor in brain injury treatment. My results demonstrate that SAWs can promote astrocyte coverage and extrusion growth without affecting width, primarily through enhanced cellular activity rather than increased membrane permeability. Overall, this thesis contributes a new analytical approach to measuring diffusion, advances our understanding of SAW-based mechanisms, and offers a novel potential treatment avenue for neurological disorders involving axonal dysfunction.
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    Improved hidden Markov models for continuous gravitational wave searches
    Clearwater, Patrick Winston ( 2022-11)
    The direct detection of gravitational waves in 2015 has ushered in a new way of making astronomical observations and provided a rich stream of data for making astrophysical inferences. The detections reported by the Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO) and the Virgo detector during their first three observing runs have so far all been compact binary coalescences, which are short duration signals from the late stages of compact object mergers. There is much left to be discovered, and this thesis advances the state of the art in searches for continuous wave signals: persistent, relatively-weak signals from sources such as neutron stars. The thesis describes two significant improvements to the hidden Markov model (HMM) scheme often used for continuous wave searches, applies the HMM to a search of LIGO Observing Run 2 (O2) data, and describes two ancillary improvements (graphics processing unit optimisation and few-bit digitisation) that improve the performance and memory-efficiency of the implementation. HMMs are used in continuous wave searches to account for spin wandering: small stochastic variations in signal frequency. They work by splitting detector data into short time segments, calculating a detection statistic as a function of frequency at each segment, and then tracking the most likely path for the signal frequency based on a user-specified transition model (an unbiased random walk in this thesis). We introduce a detection statistic called the J-statistic which is sensitive to sources that are part of a binary system. The J-statistic reliably detects signals weaker by a factor of four compared to the Bessel-weighted F-statistic, the previous detection statistic used in HMM searches for binary sources. This improved HMM scheme allows searches for binary sources to be as sensitive as searches for isolated sources. We use the J -statistic HMM pipeline, called "version 2", to search LIGO O2 data for gravitational radiation from the low-mass x-ray binary Scorpius X-1 over a 60-650 Hz frequency band. While no detection is claimed, three candidates survive our follow-up veto procedure. Assuming a non-detection, the search sets a 95 per cent confidence upper limit on strain h_0 of 3.47e-25 at 194.6 Hz when marginalising over the inclination angle of the source. One drawback of the HMM is that each time segment is combined incoherently: version 2 of the HMM does not enforce a consistent signal phase in the transition between blocks. We introduce version 3 of the HMM, which does track inter-block phase. The result is a detection pipeline, applicable to either isolated or binary sources, that is a factor of ~1.5 more sensitive than version 2, and closes much of the gap between the HMM and a fully-coherent search while retaining the computational efficiency of earlier HMM versions. We describe an implementation of the J -statistic and HMM on graphics processing units (GPUs), which provides an order-of-magnitude improvement in processing speed and was essential for covering the wide parameter range used in the O2 Scorpius X-1 search. Running that search using the GPU implementation of the pipeline required approx < 3e5 GPU-hours. We further describe the first application of few-bit digitisation techniques to continuous gravitational wave search methods, finding a decrease in sensitivity of only 6 per cent (two-bit digitisation) or 25 per cent (one-bit) in return for a factor of 32 or 64, respectively, reduction in memory use.
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    Constraining Cosmology with Secondary Anisotropies and Cluster Lensing of the Cosmic Microwave Background with the South Pole Telescope
    Chaubal, Prakrut ( 2023-06)
    There is a wealth of information encoded in the higher angular multipoles of the Cosmic Microwave Background (CMB) waiting to be explored with high-resolution observations. In this thesis I will discuss the work done during my PhD, where I used the latest data, observed with the South Pole Telescope, to measure the secondary anisotropies of the CMB. I will also discuss the use of CMB-cluster lensing as a powerful tool to constrain cosmology. In this thesis, I present the first-ever measurement of the high-\el{} temperature anisotropies from the 2019-2020 winter observations of the 1500 \sqdeg{} SPT-3G survey. I discuss the method used to obtain an unbiased measurement of the bandpowers from the low level data from the telescope. Second, I investigate the lensing of the CMB by galaxy clusters. I show the improvement to cosmological constraints from galaxy cluster surveys with the addition of CMB-cluster lensing data. I explore the cosmological implications of adding mass information from the 3.1$\sigma$ detection of gravitational lensing of the cosmic microwave background (CMB) by galaxy clusters to the Sunyaev-Zel'dovich (SZ) selected galaxy cluster sample from the 2500 \sqdeg{} SPT-SZ survey and targeted optical and X-ray followup data. In the \lcdm{} model, the combination of the cluster sample with the Planck power spectrum measurements prefers $\sig(\Omega_m/0.3)0.5=0.831\pm0.020$. Adding the cluster data reduces the uncertainty on this quantity by a factor of 1.4, which is unchanged whether or not the 3.1$\sigma$ CMB-cluster lensing measurement is included. We then forecast the impact of CMB-cluster lensing measurements with future cluster catalogs. Adding CMB-cluster lensing measurements to the SZ cluster catalog of the on-going SPT-3G survey is expected to improve the expected constraint on the dark energy equation of state w by a factor of 1.3 to $\sigma(w)$=0.19. We find the largest improvements from CMB-cluster lensing measurements to be for \sig, where adding CMB-cluster lensing data to the cluster number counts reduces the expected uncertainty on \sig{} by factors of 2.4 and 3.6 for SPT-3G and CMB-S4 respectively.
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    Measurement of the branching fraction and CP asymmetry of B0 to pi0 pi0 decays at Belle II
    Pham, Francis Huy ( 2023-08)
    This thesis presents a measurement of the branching fraction and CP-violation asymmetry in B0 -> pi0pi0 decays. The analysis uses a sample that corresponds to 198e6 BB pairs, collected by the Belle II experiment at the SuperKEKB accelerator in Tsukuba, Japan. Among collider experiments, only Belle II can efficiently record B0 -> pi0pi0 events at rates enabling competitive measurements to previous results. The large uncertainties of the branching fraction and CP-violation asymmetry of B0 -> pi0pi0 decays are the greatest limitation in determining the least known angle of the unitarity triangle, phi2. To enhance the precision of the B0 -> pi0pi0 measurement, this analysis employs improved machine learning algorithms to suppress misreconstructed photons and continuum background. Simulated samples are used to optimise event selection criteria, compare observed data distributions with expectations, study background sources, and model distributions. The branching fraction and direct CP asymmetry are extracted from a three-dimensional unbinned extended maximum likelihood fit simultaneously to events divided into seven data sets. The measured branching fractions and direct CP asymmetries are: B(B0 -> pi0pi0) = (1.38 +- 0.27 +- 0.22) x 10-6 ACP(B0 -> pi0pi0) = 0.14 +- 0.46 +- 0.07 where the first uncertainty is statistical and the second uncertainty is systematic. These values are in agreement with previous results. The statistical and systematic uncertainty of the B measured in this work is similar in size to those obtained by Belle despite using a dataset almost a quarter in size. This demonstrates Belle II's potential for high-precision measurements of charmless hadronic B decays measurements, enabling the parameter space of new physics to be further constrained.
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    Non-Equilibrium Processes in Neutron Stars and Ultracold Gases
    Kerin, Alex David ( 2023-06)
    From the booms and busts of the economy to the schooling of fish, non-equilibrium phenomena are ubiquitous and appear at all scales. However, non-equilibrium systems have proven infamously difficult to model and understand. In this thesis we present two different of non-equilibrium systems, one classical and one quantum mechanical, and thoroughly investigate their behaviour: (i) the repeated localised mechanical failure of the crust of a spinning down neutron star, and (ii) the dynamics of quenched few-body quantum systems. As an isolated neutron star spins down the centrifugal force weakens but the gravitational force doesn't change. This results in the crust changing shape and accruing mechanical strain to the point of failure. Mechanical failure locally deforms the crust and dissipates and redistributes strain. This can result in avalanches of further failures as one region of the crust failing may prompt a neighbouring region to fail. The evolving crust is a classical far-from-equilibrium system capable of avalanche behaviour like the classic sandpile model. The statistics of crustal failure events are of much interest due to their suggested relevance to transient phenomenon such as glitches or fast radio bursts. We present a cellular automaton designed to describe the evolution of the crust over spin down and the effects of local failure. This automaton describes when and where crustal failures occur and how large they are. Additionally this automaton describes the failure-induced change in the shape of the crust. Using this automaton we find that the star needs to be born spinning over \approx 750 Hz to accumulate sufficient strain to fail at all, that the waiting-times between subsequent events are distributed as a power-law spanning seven orders of magnitude, and that the ellipticities of isolated neutron stars are in the range 10^{-13} to 10^{-12}, among many other results. It has been suggested that the mechanical failure of the crust is the cause (or result) of a variety of transient phenomena such as glitches or gamma ray bursts. This model provides predictions of the statistical behaviour of crustal failure which can be compared to the observed behaviour of these transients. Additionally, the model describes the shape of the crust and the rotational frequency at all times which allows for the wave strain of emitted gravitational waves to be calculated with implications for searches for continuous gravitational wave sources. Cold quantum gases have attracted a great deal of experimental and theoretical interest thanks to the high degree of experimental control possible over them which makes them excellent testing grounds of quantum theory. Additionally, they are excellent tools for the study of quantum thermalisation. We consider a few interacting particles initially in some equilibrium state and suddenly change (quench) the interaction strength which kicks the system away from equilibrium. Specifically, we consider systems of two and three bodies of arbitrary mass and various particle symmetries interacting via a contact interaction in an isotropic three-dimensional harmonic trap. We take particular interest in quenching between the weakly and strongly interacting regimes and the following far-from-equilibrium post-quench evolution. We describe the non-equilibrium post-quench evolution of the system by analytically and semi-analytically calculating two observables: the Ramsey signal and the particle separation. We are able to calculate these quantities for the two-body system with arbitrary particle masses for any quench in interaction strength. Additionally, we extend these calculations to three-body systems of two identical fermions and a distinct particle or three identical bosons where the quench is between the strongly and weakly interacting regimes. In the two-body case we find when quenching from weak to strong interactions the particle separation oscillates periodically between \approx0.85a_{\mu} and \approx1.15a_{\mu}, where a_{\mu} is the simple harmonic oscillator length-scale. For the same quench in the three-body case the particle separation varies depending on the specifics of the system. For the fermionic case the particle separation oscillates periodically, peaking at \approx 2.18a_{\mu} with the mass ratio of the two species determining the minimum separation. For the bosonic case the oscillation is aperiodic. Both the maximum and minimum particle separation are determined by a quantity called the three-body parameter, but particle separation generally oscillates between \approx a_{\mu} and \approx 2a_{\mu}. However, in all cases when quenching from strong to weak interactions the calculations of the particle separation do not converge. This divergence is present whatever the initial state, mass ratio, particle symmetry, etc. and is present only for this particular quench from strong to weak interactions. We investigate possible sources of this divergence and future avenues of research into its causes. Finally, we note that these theoretical predictions of Ramsey signal and particle separation are experimentally testable with current techniques.
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    Neutron star spin wandering and its effects on electromagnetic and gravitational wave observations
    Vargas Sanchez, Andres Felipe ( 2023-05)
    Neutron stars spin down secularly under the action of electromagnetic and gravitational wave torques. In addition, their rotational frequency can also exhibit stochastic fluctuations over time, commonly known as spin wandering or timing noise, through several mechanisms. This thesis aims to explore the effect of spin wandering on electromagnetic and gravitational wave observations of neutron stars. Rotating neutron stars offer great potential as targets for continuous gravitational wave (GW) searches using data from terrestrial observatories such as the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO), Advanced Virgo, and the Kamioka Gravitational Wave Detector (KAGRA) (collectively known as the LVK collaboration). As these searches aim to track the GW frequency, which is related to the spin frequency in many emission mechanisms, it is crucial to accommodate spin wandering in the search algorithm. A possible approach is to deploy a hidden Markov model (HMM) which postulates that the GW frequency executes a random walk. In this thesis we present the outcome of two GW searches using a HMM-based pipeline that accounts for spin wandering. The first search, conducted as part of the LVK collaboration, targets the low-mass X-ray binary (LMXB) Scorpius X-1 using data from LIGO's third observing run (O3). Within the band from 60 Hz to 500 Hz, we find no candidate that survives following a two-step vetoing procedure and follow-up process. We infer the most sensitive upper limits on gravitational wave strain at a 95% confidence level, h0^95%, for HMM-based Scorpius X-1 searches. The most sensitive 0.61 Hz sub-band, starting at 256.06 Hz, achieves h0^95%=6.16E-26 when assuming the source's electromagnetically constrained orbital inclination angle of iota=44 degrees. This is the first Scorpius X-1 HMM-based search that yields upper limits below the indirect torque-balance limit for certain sub-bands, assuming iota=44 degrees. The second search targets the millisecond pulsar PSR J0437-4715 using data from O3. The target is selected because it is relatively close to the Earth (distance 156.3+/-1.3 pc), and its rotational and orbital parameters are known to high accuracy from radio pulsar timing. This is the first search for PSR J0437-4715 to cover a wide frequency range, from 60 Hz to 500 Hz, while allowing for spin wandering. Two analyses with plausible spin-wandering timescales, 10 days and 30 days, are conducted. The former analysis yields no surviving candidate, while the latter yields five surviving candidates after the vetoing and follow-up procedures. All surviving candidates appear in sub-bands not covered by previous analyses. Future searches, e.g. using the upcoming LVK fourth observing run, will shed more light on the nature of these five survivors. The secular spin down of rotationally-powered pulsars is thought to be governed by the power-law braking torque, dotnu proportional to nu^n_pl, where \nu is the spin frequency, the overdot indicates a time derivative, and $n_pl is the braking index. The value of n_pl specifies the spin down mechanism, such that n_pl=3 denotes vacuum magnetic braking, n_pl=5 denotes GW radiation, among others. Measuring n_pl for a pulsar involves measuring nu, dotnu, and ddotnu, via high-precision pulsar timing over years or decades. However, spin wandering can mask the secular behavior of nu, dotnu, and ddotnu over such long time-scales. This may be part of the reason why certain pulsars exhibit anomalous braking indices | n | = | nu ddotnu / dotnu^2 | >> 1. This thesis quantifies how timing noise affects the accuracy with which the secular braking torque can be measured. We show through analytic calculations, Monte Carlo simulations involving synthetic data, and modern Bayesian techniques, that the variance < n^2 > of the measurements of n scales with the square of the timing noise amplitude sigma^2_ddotnu. For astrophysically relevant values of sigma^2_ddotnu, the dispersion of n is typically greater than the formal uncertainty Delta n associated with a measurement of n, and the value of n_pl used to generate the synthetic data. For example, for sigma^2_ddotnu= 1E-56 Hz^2 s-5 at least 50% of the [n-Delta n,n+Delta n] intervals include n_pl, while for sigma^2_ddotnu=1E-50 Hz^2 s^-5 this percentage drops to 8%. We present a theoretically derived and observationally testable inequality, which sets the threshold for the anomalous regime < n^2 > >> 1, and expresses the minimum sigma_ddotnu^2 corresponding to the anomalous regime < n^2 > >> 1 in terms of observables such as nu, dotnu, a stellar damping time-scale gamma_ddotnu, and the total observing time T_obs.