Fall 2020

Fall 2020

  • A Bootstrapper’s Guide to Conformal Field Theory

  • Brilliant Ideas in Condensed Matter Physics

  • Data-Driven Approaches to Physical Systems

  • Designing an Experiment

  • Diagrammatics and Linear Response in Condensed Matter Theory

  • Geometric Quantization

  • Group Theory and Quantum Mechanics

  • Integrated Photonics with Single Photon Emitter

  • Intro to Strongly Correlated Electron Systems

  • Introduction to Topological Insulators

  • Mathematical Foundations of Quantum Mechanics

  • Modeling Neural Behavior

  • Relations between Classical and Quantum Mechanics

  • The Role of Mathematics in Physics Education Research


A Bootstrapper’s Guide to Conformal Field Theory with Ryan Lanzetta

Quantum field theories with conformal symmetry, known as conformal field theories, are among the most well understood quantum field theories. Conformal field theories are central to many areas of physics, from continuous phase transitions in statistical and condensed matter systems to string theory. In roughly the past decade, the modern, numerical conformal bootstrap research program has revolutionized the study of conformal field theories. This quarter, we will briefly motivate our study of conformal field theory by touching on the set of ideas known as the renormalization group. Then, we will study conformal field theory proper and perform some numerical calculations with the conformal bootstrap technique, focusing on theories in one spatial dimension.

Reading: Excerpts from “Lectures on Statistical Field Theory” - David Tong and “Aspects of Two-Dimensional Conformal Field Theories” - Xi Yin; Supplement with “Conformal Field Theory” - Di Francesco et. al. and research papers as necessary, depending on student interest.

Requirements: Phys 325 (QM 2), PHYS 328 (Stat Mech) (No background in quantum field theory necessary!)

Recommended: Computer programming experience, familiarity with the theory of groups and their representations


Brilliant Ideas in Condensed Matter Physics with David Rosser

Have you ever thought thermodynamics and statistical mechanics are the bee’s knees? Or felt the path integral is the greatest thing since sliced bread? Maybe you have fallen asleep at night wondering how in the world did Lars Onsager solve the two-dimensional Ising model? If you have said yes to any of these questions, then this is the reading course for you.

Prerequisites: Quantum and Statistical Mechanics

Textbook: Quantum field theory and condensed matter by Ramamurti Shankar, Chapters 1-8


Data-Driven Approaches to Physical Systems with Olivia Thomas

Data-driven modeling is increasingly used to study the multi-scale structure and dynamics that characterize complex physical systems. We will start by exploring general techniques such as principal and independent components analysis, and then move on to more specialized applications (fluid flows, atmospheric science, biophysics, etc.) and methods based on the student’s interest. Studying these techniques can deepen your understanding of the physical system that interests you and also broaden your analytical skill set.

Reading: “Data-Driven Science and Engineering” by S. Brunton and J. N. Kutz (book), assorted papers TBD

Prerequisites: MATH 307 (Intro to Differential Equations), MATH 308 (Linear Algebra)


Designing an Experiment with Joshua Labounty

So you want to measure something? How do you actually go about doing so? Using publications from the Muon g-2 Experiment, the Axion Dark Matter Experiment (ADMX), the Stern-Gerlach Experiment, and others as guides we will dive into the principles which underly good experimental design, and see which pitfalls to avoid. We will also use the technical design report from the Muon g-2 experiment to get a glimpse into the technical side of development, from constraints on a data acquisition system to predicting backgrounds. Using that knowledge and guided by student interest, we can then go about creating a simple experiment (say, a measurement of the speed of light) from first principles.

Reading:

https://plato.stanford.edu/entries/physics-experiment/

Papers: Stern-Gerlach: https://plato.stanford.edu/entries/physics-experiment/app5.html and https://www.semanticscholar.org/paper/Stern-and-Gerlach%3A-How-a-Bad-Cigar-Helped-Reorient-Friedrich-Herschbach/98fb597d99abf4f0d4e94118377d501f2777cb5c

E821 Muon g-2 PRD: http://dx.doi.org/10.1103/PhysRevD.73.072003

Sections of the E989 Muon g-2 Technical Design Report: https://arxiv.org/abs/1501.06858

ADMX: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.101303 and https://arxiv.org/pdf/1804.08770.pdf

Others TBD based on student interest

Requirements: Completion of 12x physics series. PHYS 225 (Introduction To Quantum Mechanics)

Suggested: One or more 32x physics courses (Electricity and Magnetism, Quantum Mechanics, Statistical Physics, etc.)


Diagrammatics and Linear Response in Condensed Matter Theory with Michael Smith

Many interesting problems in physics start with taking a well known system and applying a symmetry breaking perturbation (such as an electric or magnetic field). But how do we calculate the response of materials in the presence of (sufficiently small) symmetry breaking fields? In this project we will explore linear response theory, starting with an introduction to Green’s functions, their relationship to physical observables, and their equations of motion in the presence of interactions and impurities, which will help us formulate the diagrammatic rules necessary for linear response. The second half of this project will focus on using these Green’s functions to calculate linear response coefficients, such as the electrical conductivity, via the Kubo formula

Reading: “Quantum Transport Theory” by Jorgen Rammer, Ch. 2,3,4, and 7

Requirements: PHYS 228 (Math Methods 2), PHYS 324 (QM 2), PHYS 322 (EM 2), Phys 329 (Stat Mech)

Strongly Recommended: PHYS 423 (Condensed Matter)


Geometric Quantization with Michael Clancy

The advent of quantum mechanics came with a number of interpretive problems. Perhaps the easiest to see comes from the uncertainty principle: any quantum state on a nontrivial system does not allow for all observables to have determined values. This is far more problematic than typical Bayesian uncertainty: it’s not that we don’t know what the position is, it’s almost like the position doesn’t even know what it wants to be. Since quantum theory is the most effective tool for predicting the outcomes of experiments, it cannot be helped that the interpretive parts are shaky at best. One way of remedying discomfort with this shortcoming is by connecting quantum mechanics with its more physically interpretable classical counterpart. Geometric quantization refers to the systematic approach of associating Hilbert spaces to symplectic manifolds.

The first few weeks of the quarter will be devoted to reviewing classical and quantum mechanics in the context of symplectic manifolds and Hilbert space theory. After that, we will follow a set of notes which provide a crash course on geometric quantization. My plan is for the climax to be connecting the opaque mathematical “integrality” condition in quantization to the fact that particles can only have half-integer spin.

Reading: Geometric Quantization: A Crash Course (Eugene Lerman), Introduction to Smooth Manifolds (Lee)(supplemental), various papers

Prerequisites: PHYS 325 (QM 3), PHYS 329 (Classical Mechanics), MATH 340 (Abstract Linear Algebra)


Group Theory and Quantum Mechanics with Tyler Blanton

Symmetries play a fundamental role in all branches of physics, yet in introductory courses they are often glossed over or only discussed qualitatively. A big reason for this is that to fully appreciate the impact of symmetries at a quantitative level, one needs to first obtain a basic understanding of some of the (sometimes abstract) mathematics of group theory, which is not part of the core math sequence and is often a blind spot for physicists. In this project, the aim is to introduce group theory as a means of understanding how fundamental symmetries in nature give rise to physical phenomena such as conservation laws, selection rules, and energy splitting. I suspect we will spend some time examining quantum mechanics in crystals/lattices, but the exact scope of the project is very flexible.

Reading: Online references (TBD)

Requirements: PHYS 324 (QM 1), strong interest in math

Strongly Recommended: PHYS 325 (QM 2), PHYS 227-228 (Math Methods 1-2)


Integrated Photonics with Single Photon Emitters with Christian Pederson

Solid-state systems that emit single photons (e.g. color centers, quantum dots) are an extremely useful resource in a number of quantum applications, due to their ability to entangle distant qubit systems. Integrating these emitters into photonics is not only necessary for efficient collection and routing but also allows for precise control over fundamental properties of the emitted light. In this course, we will study the theory behind single-photon emission and investigate various experimental realizations of integrated single quantum emitters.

Readings: "Quantum Optics", Scully and Zubairy, "Quantum Photonics Incorporating Color Centers in Silicon Carbide and Diamond", Radulaski and Vučković

Papers: TBD

Prerequisites: PHYS 322, PHYS 325


Intro to Strongly Correlated Electron Systems with Arnab Manna

Strongly correlated electron systems are among the central themes for much of the condensed matter physics developments in recent history. These materials contain highly-coupled charge, spin, orbital, and lattice degrees of freedom, which conspire to produce interesting emergent states and behavior including high-temperature superconductivity, colossal magnetoresistance, metal-insulator transitions and magnetism. In this project, we will explore some of the basic models to explain correlated electron phenomena that are not captured by “independent” electron approximations (Fermi Liquid theory) and then briefly learn about the insights provided by various recent experimental studies in these systems.

Reading: “Lessons from Nanoelectronics” by Supriyo Datta, various papers

Prerequisites: PHYS 324,325 (Quantum 1&2)

Recommended: PHYS 423 (Condensed Matter), PHYS 329 (Stat Mech)


Introduction to Topological Insulators with Qianni Jiang

The concept of topological order represents a new paradigm in condensed matter physics. Topological insulators, as a representative example of the topological phases, are insulating in their interior but conductive in their topologically protected surface/edge states. Knowledge about topological insulators will help you understand many other cutting-edge topological phases, such as Dirac semimetal, Weyl semimetal, topological superconductor, and quantum anomalous Hall effect. In this project we will start from the basic band theory of solids and the concept of topology in condensed matter physics. Then we will have a historical review on the theoretical and experimental progress in realizing 2D and 3D topological insulators. At last, we will introduce the basic idea of some other related topological phases based on student’s personal Interest.

Reading: Ashcroft and Mermin, Solid State Physics, Chapter 4,5, 8, 9.

M. Z. Hasan and C. L. Kane Rev. Mod. Phys. 82, 3045 (2010).

Requirements: PHYS 325, PHYS 322, PHYS 328

Recommended: PHYS 423


Mathematical Foundations of Quantum Mechanics with Kade Cicchela

The modern mathematical foundation of quantum mechanics involves mathematical structures which are not typically presented in a physics curriculum. In particular, topics within functional analysis such as operator theory and spectral theory are of great importance. In this reading course, we will explore the use of functional analysis in quantum mechanics with a focus on mathematical clarity. More abstractly, we will consider how the kinds of mathematical structures that are used in a physical theory are determined by the kinds of statements that theory needs to make and the results of relevant experiments. Topics that might be covered include: Operator Theory, Spectral Theory, Stone-von Neumann Theorem, Wigner’s Theorem, Representation Theory, C*-algebras, Quantization, Measurement, Projection-valued Measures, POVMs, Gleason’s Theorem, Interpretations of Quantum Mechanics, Topos Theory.

Reading:

  • An Introduction to the Mathematical Structure of Quantum Mechanics by F. Strocchi

  • Mathematical Methods in Quantum Mechanics by Gerald Teschl

Requirements: PHYS 325 (QM 2), some proof-based math course

Recommended: PHYS 329 (Classical Mechanics), MATH 340 (Linear Algebra)


Modeling Neural Behavior with John Ferré

The brain is a giant, unsolvable, electrical circuit that generates an enormous array of responses from any given stimuli. While we are a long way from completely understanding the brain, neuroscientists have found many interesting results: from basic circuit models to network models that can help explain abstract thoughts. To explore these results, we will first learn about the underlying physics that generates complex neural responses. Afterwards, we will explore modeling approaches of neural responses and understanding various physical behaviors at the neuron level.

Reading: Dayan and Abbot: Theoretical Neuroscience, papers TBD

Requirements: PHYS 228, PHYS 322


Relations between Classical and Quantum Mechanics with Joseph Merritt

Quantum mechanics is a subject which is considered by many to be mysterious and unintuitive. A major reason is that the basic workings of quantum mechanics differ greatly from the classical mechanics of everyday experience. And yet, it is widely believed that quantum mechanics must at some point “turn in to” classical mechanics, since they both accurately describe different aspects of our world. In this project we will explore how these two theories are related to each other, covering topics such as the methods of creating quantum models from classical equations, and seeing ways that classical mechanics can come from reducing quantum theories.

Reading: “What is the limit ‘h to 0’ of quantum theory?” by U. Klein (on arXiv) and other articles TBD

Prerequisites: PHYS 324; some familiarity with classical mechanics preferred


The Role of Mathematics in Physics Education Research with Charlotte Zimmerman

Quantitative reasoning, or how we make sense of the world through the application of mathematics, is essential to “thinking like a physicist” and therefore at the heart of much of our undergraduate physics curriculum. Recent work in physics education research suggests that physics and mathematics are so cognitively intertwined that they cannot be separated, yet “math in math class” is distinctly different from “math in physics class.” Together, we will explore how mathematics manifests in undergraduate physics curriculum and the education research that is being conducted to better understand how students are using quantitative reasoning and how we can improve our courses. As this topic is being explored at all levels of physics education, from high school through undergraduate quantum mechanics, our direct focus will be determined by the participant’s interest.

Reading:

[1] Sherin, B. L. (2001). How Students Understand Physics Equations. Cognition and Instruction, 19(4), 479–541.

[2] Redish, E. F., & Kuo, E. (2015). Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology. Science and Education, 24(5–6), 561–590.

Requirements: Experience in the subject you would like to explore (i.e. if you are interested in the introductory sequence, all you need is completion of 12X. If you are interested in the linear algebra of quantum mechanics, you’ll need to have completed Phys 324 and 325.)