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Stability of Quantum Many-Body Systems
Full text linkIn quantum many-body systems subjected to generic perturbations, eigenstates are typically fragile and prone to strong mixing, leading to rapid thermalization in dynamics to an equilibrium state described by statistical mechanics. However, there exist robust counterexamples that defy this typical expectation, exhibiting novel non-equilibrium phenomena and offering potential applications in (quantum) information processing. This dissertation explores such systems and establishes their stability against perturbations with mathematical rigor.
First, by generalizing the exponentially slow tunneling effect in single-particle quantum mechanics, we develop a theory of metastability in quantum many-body systems, demonstrating their nonperturbatively long lifetimes. As a canonical application, we provide the first general and tight bounds on the slow decay of false vacua.
Second, it is known that ground states in finite spatial dimensions can resist arbitrary local perturbations through topologically ordered phases of matter. We extend this notion of stability to quantum error-correcting codes in infinite dimensions, specifically quantum low-density parity-check (LDPC) codes. These codes are of significant interest due to their promise of lower fault-tolerance overhead compared to finite-dimensional codes.
Lastly, we analyze classical counterparts of LDPC codes and prove that their eigenstates remain localized in the many-body Hilbert space under generic perturbations. This finding presents the first unambiguous example of a robust violation of the eigenstate thermalization hypothesis.
To achieve these results, we introduce advanced techniques to control operator locality, leveraging and generalizing methods such as Lieb-Robinson bounds, cluster expansions, and Schrieffer-Wolff transformations. These tools not only underpin our specific findings but may also prove valuable for broader challenges in mathematical physics of quantum many-body systems. </p
Rise Over Run: The Rise of AI and the Run on Personal Information
Full text linkTechnological revolutions have always been double-edged swords. Just as electricity brought both illumination and electrical hazards, and the internet enabled both connectivity and surveillance, large language models (LLMs) represent both an extraordinary leap in artificial intelligence (AI) and a profound risk to privacy. These models, capable of generating human-like text, are rapidly being deployed across industries—from automating customer service to shaping critical business decisions. Yet, beneath their polished outputs lies an unresolved vulnerability: the potential for personally identifiable information (PII) leakage. Whether through unintended memorization, adversarial prompting, or the compounding risks of fine-tuning and retrieval-augmented generation (RAG), LLMs can become conduits for privacy breaches on an unprecedented scale.
This thesis systematically examines these risks through empirical testing, evaluating how different LLM architectures respond to adversarial attacks and assessing the efficacy of existing safeguards. By framing LLMs as critical infrastructure—essential yet vulnerable—this research highlights the urgent need for security measures that evolve alongside the technology itself. Just as power grids required circuit breakers and the internet demanded encryption, the proliferation of AI demands robust privacy-preserving mechanisms. Ultimately, this thesis argues that as LLM technology advances, so too do its privacy vulnerabilities. The challenge is not to halt progress but to ensure that responsible AI innovation balances this rapid advancement with the necessary safeguards to protect personal data and maintain public trust. </p
Learning to Become Language Policy Actors: A Qualitative Longitudinal Study of Bilingual Special Educators in Synchronous-Service Teacher Preparation
Full text linkSynchronous-service preparation (SSP), a form of teacher education that places beginning teachers immediately in roles as teachers of record, has provided a heavily relied upon policy mechanism to address the pressing problem of US teacher shortages. Given that shortages tend to be concentrated in certificate areas targeting students labeled English Learners and students with disabilities, there is a growing number of educators certified through SSP working in highly specialized roles. These teachers are meant to provide legally mandated language and Special Education services, yet the impact of SSP on teacher learning has gone relatively unexamined.
This dissertation study explores the interlocking relationship between education policy and SSP teacher learning in the context of Bilingual Special Education. Using queer theory and a critical, sociocultural policy framework, I leverage a qualitative longitudinal research design informed by anti-oppressive methodology to journey alongside a cohort of Latinx bilingual special educators in SSP. This study specifically reports on teachers’ learning as SSP graduates by asking: 1) How do teachers make sense of their experiences becoming teachers through SSP?; and 2) What are the questions and uncertainties that teachers hold about their practice four years later?
Findings illustrate how teachers used SSP to gain access to the profession while maintaining commitments to communities with whom they shared deep social ties. Teachers expressed uncertainty around their responsibilities as bilingual special educators in local school contexts, an ambiguity they felt to be under-supported within and beyond SSP. Teachers were also navigating a policy context in which they were learning to adapt district-mandated curricula for bilingual students and students with disabilities.
My dissertation findings hold implications for studying teacher learning longitudinally and examining teacher preparation in relation to education policy. The project offers an example of how teacher education research can account for what policy does to teachers beyond formal boundaries of preservice teacher preparation. Importantly, the study also centers the perspectives of Latinx Teachers of Color and advocates for a policy stance that prioritizes the desires of these teachers alongside attempts to address shortages.</p
Thorium-229 Nuclear Clock Using a VUV Frequency Comb
Full text linkLaser-based measurement and control of atomic and molecular states form the foundation of modern quantum technology and provide deep insights into fundamental physics. Today’s most precise clocks are based on measurements of optical transitions in atoms. To this end, transitions with high quality factors, low sensitivities to external perturbations, and good signal-to-noise ratios are desired.
In this thesis, we achieve frequency-based laser spectroscopy of the 229Th nuclear clock transition using a vacuum ultraviolet (VUV) frequency comb. The high transition frequency of 2,020,407,384,335(2) kHz (in 150 K CaF2 crystals) and a long excited state lifetime of 641(4) s show the high intrinsic quality factor of this nuclear transition. This transition frequency is pre�dicted to be insensitive to external perturbations due to 1) the small electromagnetic moment of the atomic nucleus and 2) the shielding effect of the outer electronic shell. Further, the large number density of quantum emitters in a solid-state crystalline host promises a high signal-to-noise ratio. Moreover, based on the different fundamental interactions involved in nuclear versus electronic transitions, precise comparisons between nuclear and atomic clocks offer dramatically enhanced sensitivity to new physics. Resolving individual nuclear quantum states in its host crystal enables us to perform the first steps in characterizing the nuclear clock performance.
Probing the 229Th nuclear transition required new tools. Building upon previous generations of extreme-ultraviolet (XUV) comb projects in our lab, we construct a VUV comb to perform direct frequency comb spectroscopy of the 229Th nuclear clock transition. We calibrate the absolute frequency by linking this comb to the JILA 87Sr atomic clock. We also present our effort in making 229Th thin-film samples for reducing the cost and radioactivity of future nuclear clocks. </p
Generating a Trajectory From Sun-Earth L1 to L4 via Reinforcement Learning
Full text linkReinforcement learning is widely used in path-planning applications, where an agent learns to achieve a task by exploring its environment. This idea can be extended to use in spacecraft trajectory design as well since it is a similar problem statement. Autonomous trajectory design is an area of growing importance given the rise of faster and more efficient computers and concepts of artificial intelligence and machine learning. In this thesis, the Proximal Policy Optimization (PPO) algorithm is used to design a trajectory in the Sun-Earth Circular Restricted Three Body Problem (CR3BP). PPO has been widely used in the astrodynamics community for such trajectory design problems due its ability to efficiently handle continuous action spaces and maintain stable learning through the use of a clipped objective function, which prevents excessively large updates to neural network parameters. This thesis is inspired by sun-observing missions. There have been multiple missions to observe and gain a better understanding of the processes that drive the heat and light generation of the Sun, and collect data to predict solar storms that originate below or close to its surface. Solar storms have a lasting impact on all bodies enveloped in the heliosphere, including the Earth and its satellites. When observing a celestial body, it can be desirable to have the observatory placed in an orbit that will require minimal station-keeping while maximizing observation opportunities and enabling uninterrupted data collection. For a solar observation mission to narrow down sources of solar energetic particles, a desirable location is the L4 lagrange point. However, the spacecraft may need to reach this location from an orbit. For these reasons, this thesis explores the use of PPO to design a trajectory from an L1 Lyapunov orbit to the vicinity of L4.</p
Leaning Into the Discomfort of School Reform: A Reflective Teacher Leader Attends to the Whole Educator and Affective Spaces in Professional Learning Cycles
Full text linkSupporting schools that have been determined to be underperforming is rife with challenges, particularly given that the methods for enacting rapid, significant reform create difficult atmospheres in which to enact change, with potential for high levels of distrust, increased workloads, stressors, and uncertainty. This qualitative study traced the design and enactment of professional learning cycles for high school Humanities teachers, including the iterations and adaptations of sessions based on teacher needs and goals, and my reflections and learnings as a teacher leader researcher who was embedded in the school site. Drawing from collaborative professional learning, culturally and historically responsive pedagogy, and practitioner inquiry frameworks, this study explored the experiences of a team of high school Humanities teachers, school leaders, and students in their urban, alternative school’s first full year of turnaround. I describe the ways in which the professional learning design and facilitation shifted based on the learning that showed up in teachers’ praxis, school stakeholders’ perception of the change that they experienced, and my noticings of teachers’ and my own affective responses to our collaborations. Three major themes emerged from the study, all surrounding the need for leaders to pay attention and adjust when necessary related to teachers’ learning processes, teachers’ praxis, and the way all participants (teachers, leaders, and students) were engaging with and feeling about change. These findings and themes hold implications for school leaders, districts, and researchers leading school reform.</p
Quantitative Analysis of Alpine Skis Using Distributed Sensing and Modal Analysis
Full text linkIn the alpine skiing industry, product development and product evaluation are typically conducted using qualitative evaluation; this leads to a relatively inefficient, time-consuming, and imprecise design and testing cycle. A multitude of studies have collected quantitatively relevant data for alpine skis, but most captured singular components in isolation, and there have not been many attempts to marry them all together into a comprehensive qualitative analysis framework.
The grail for qualitative analysis in alpine skiing is the formation of relevant in-situ loading scenarios. Many attempts to create an accurate finite element model (FEM) have been made; most have proven their validity in laboratory settings, but none have proven their validity across a wide range of in-field skiing scenarios due to the lack of available in-situ loading scenarios. The main issue limiting in-situ force estimation is the extreme difficulty of accurately depicting boundary conditions for all phenomena experienced in skiing, making it an ill-posed problem.
This study proposes the use of laboratory modal analysis, in-field modal analysis, and stiffness profile measurements to capture natural frequencies, damping ratios, mode shapes, energy storage and release behaviors, and stiffness distribution profiles to create a complete mechanical and dynamic property profile of an alpine ski for use in quantitative analysis without the need for in-situ loading scenarios. This study will also present an attempt at in-situ displacement and force estimation using a low-cost, portable/lightweight, noninvasive, and robust IMU-based sensing system but has come to the conclusion that IMUs in isolation are not capable of estimating in-situ force accurately. Force estimation validation testing has uncovered the need for more focused testing to accurately depict the relationship between the displacement and acceleration an alpine ski experiences when forces of varying loading rates and durations are applied. This testing can further refine the assumptions made for future in-situ force estimation frameworks. </p
Plato's Anti-Harm Principle
Full text linkPlato, in dialogues such as Crito and Republic I, maintained a radical anti-harm principle (AHP): one ought never to harm oneself or another, for harming is always unjust. In this dissertation, I explain the meaning of AHP, describe and evaluate Plato's arguments for it, and situate it within the broader framework of Platonic ethics.
In Chapter 1, I provide historical background and discuss anti-harm thinking in Plato's predecessors and successors. Most signicantly, I argue that Xenophon's Socrates joins Plato's Socrates in opposing all harm, though Xenophon himself does not. In Chapter 2, I counter a common suggestion about AHP, namely that Plato must have carved out "justied harms" to account for cases of self-defense, war, and legal punishment. I argue that the Crito does not support this reading by showing how Socrates's anti-harm ideals dier from the more traditional mores defended by the Laws of Athens. In Chapter 3, I describe more precisely the scope and nature of Socratic harm, and I analyze the argument for AHP given in Republic I. I conclude that, contra much recent scholarship, Republic I does not show us that Socratic harm is limited to corruption of the soul's virtue; rather, the iniction of any evil is harmful. Thus, AHP retains its full radical character. Chapter 4 contains my solution to a central problem: why would anyone endorse a principle that looks as naive as AHP does? I argue that, according to a Platonic metaphysics of causation, only the good can benet, and only the bad can harm; thus, a good character guarantees that we are not responsible for harming. We can adhere to AHP if we are able to purify our characters, and the principle gains considerable plausibility. In Chapter 5, I describe how Plato thought such purication might be possible by outlining his ideal of godlikeness. I argue that, just as the gods never harm anyone and cause all goods, the person who imitates them to the utmost extent humanly possible will also be both benecent and non-malecent. Finally, I conclude by discussing how Plato thought AHP might t into political life: what concessions must rulers and legislators make under non-ideal political conditions so that citizens who cannot be entirely prevented from harming one another nonetheless harm one another as little as possible?</p
Plural Floor Navigation by CDL Truck Drivers in the Front Range
Full text linkThis paper analyzes conversations of CDL truck Drivers in the Front Range and how these truck drivers negotiate plural speaking floors during customer interactions. For this, I collected audio recordings of multi-person phone calls between truck drivers during their work shifts over an eight-month period. The analysis of the data collected for this study concludes that CDL Truck drivers are adept at navigating plural conversation floors that occur simultaneously. This proficiency is evident in the absence of miscommunication, overlap, and misunderstandings within the conversation, despite the multi-floor structure.</p
Supervised and Unsupervised Methods for Transcriptional Sequencing Data
Full text linkIn human biology, understanding how the information encoded in an individual’s genome regulates development and responds to environment and disease remains a key question. Characterizing the differential usage of functional elements of the genome is a significant challenge, and has been advanced substantially through developments in sequencing protocols. Through a variety of sequencing protocols, we now have the ability to assay not only DNA sequence but also a wide variety of functional events and states, such as protein binding, chromatin accessibility, and RNA levels. Of particular interest are protocols measuring nascent transcription, which provide information on both the cell’s actively used regions of DNA as well as a subset of transcription factor binding events. Chemical and biological limitations in the measurement of nascent transcription mean that it remains difficult to effectively dissect the heterogeneity present from biological variation in transcriptional sequencing data. In this thesis, I develop three distinct approaches using supervised and unsupervised machine learning to address this limitation. First, I propose a novel Bayesian re-framing of sample normalization that enhances normalization in samples with external controls and allows for approximation of normalization in samples at short time points without spike-in controls. Next, I establish the feasibility of supervised deconvolution (estimating the mixing proportions of constituent cell types) in bulk nascent transcriptional sequencing data using established techniques, finding that non-coding regulatory regions both enhance model accuracy and confound estimation when undifferentiated cell types are present in the mixture. Finally, I develop an unsupervised method for discovery of cell type specific regulatory motifs using approaches drawn from language modeling, deep learning, and mechanistic interpretability. Collectively, this work advances our ability to extract useful information from nascent transcriptional sequencing data and to better understand the heterogeneity within.</p
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