Fall 2021
Fall 2021
Dynamical Systems in the Brain
Examining the structure of DNA: from polymer chain models to modern imaging techniques
Group Theory and Representation Theory in Physics
Introduction to Lambda-CDM Cosmology
Renormalization in Statistical Physics
Scattering probes (x-ray, neutron) of quantum materials
Theories of dense nuclear matter
Dynamical Systems in the Brain with John Ferre
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. One collection of models are dynamical systems, which describe the evolution of a system in an abstract space. After first learning about the basic neuroscience, we will explore various behavior, such as eye motion or memory, in terms of a subset of dynamical systems known as attractor networks.
Reading: Hopfield 1982, Mante 2013 + NMA Videos + Papers TBD
Requirements: Phys 228, Phys 322
Examining the structure of DNA: from polymer chain models to modern imaging techniques with Isaac Shelby
In this project we will cover a wide range of topics, all with the focus of understanding DNA. This is all flexible but a rough plan is to cover some background topics such as probability distributions and their moments, random walks, Brownian motion, and some basic DNA structure. Then moving into some pencil and paper calculations we will approach different polymer chain models and examine their implications. Then we can move into reading research papers on DNA imaging experiments, DNA looping, and DNA force extension.
Reading: The reading will be mostly small sections of papers, sets of online notes, and full papers towards the end of the course. Specific selections will be curated to the student’s interests. Example: Dr. Silke Rathgeber's Polymer Physics Lectures, specifically lecture 3.
Requirements: Math 125 or 135 (integral calculus) and Phys 224 (Thermal and Statistical Physics)
Group Theory and Representation Theory in Physics with John Goldak
Group theory and representation theory form an indispensable backbone for theoretical physics. In particular, many physical systems have special symmetries that reduce the complexity of the system in question. Group theory allows us to formalize much of what we mean when we say certain systems have symmetry, and representation theory then takes this a step further and adds linear algebraic concepts to compute physically relevant quantities. In particle physics, for example, you might hear that "the gauge group for the strong force is SU(3)": there is so much information packed into this seemingly tame statement, and group theory is absolutely needed to understand the wide array of ideas it conveys! The goal for this project is to introduce you to the study of group theory and representation theory, as used by physicists, so that you too can see the unexpected unity of seemingly disparate physical ideas, all united under this beautiful mathematical framework.
Reading:
Primary reference: Group Theory in a Nutshell for Physicists - Anthony Zee
Secondary references: Lie Groups, Lie Algebras, and Representations - Brian Hall; Lie Algebras in Particle Physics - Howard Georgi
Requirements: PHYS 227
Recommended: PHYS 324; experience with abstract mathematics and proofs
Introduction to Lambda-CDM Cosmology with John Franklin Crenshaw
The "concordance model" of cosmology, Lambda-CDM, has had great success describing the origin, contents, and evolution of the universe. This story begins with the fiery Big Bang, proceeds through structure formation under the influence of Dark Matter, and continues with the modern accelerated expansion driven by Dark Energy. The student will learn the basics of Lambda-CDM cosmology, as well as the open questions and tensions that exist, positioning them to understand the motivations of modern cosmology research.
Reading:
Cosmology by David Tong
Introduction to Cosmology by Barbara Ryden (provided by guide)
Requirements:
Physics 224 and 225
At least one 300-level physics course
Renormalization in Statistical Physics with Michael Clancy
Renormalization plays a central role in quantum field theory, allowing us to tame the infinities that would otherwise render QFT useless. It wasn't well understood until the 1970s, where its connection to problems in statistical physics were demonstrated by Ken Wilson.
In this vein, one does not need to study quantum field theory to learn some really cool facets of renormalization. In this project we will study some simple examples of the renormalization group - particularly we will begin with block spin renormalization.
Reading:
Scaling and Renormalization in Statistical Physics by John Cardy
The Renormalization Group and the epsilon expansion by Kenneth Wilson, John Kogut
Requirements: Phys 325 (Quantum Mechanics II), Phys 328 (Statistical Physics), Phys 329 (Classical Mechanics)
Scattering probes (x-ray, neutron) of quantum materials with Paul Malinowski
Scattering probes of condensed matter systems provide essential information about the structure, excitations, and spatial correlations within a material. In this project, we will learn the theoretical background underlying x-ray and neutron scattering in solid state systems as well as learn the details about how these experiments are actually performed. We will also read papers from the current literature on how these techniques are applied towards understanding certain quantum materials, such as unconventional superconductors, quantum magnets, density waves, and topological materials. Depending on student interest, this course can be more heavily weighted towards either theoretical or experimental focus.
Reading:
Modern Condensed Matter Physics by Girvin and Yang (Chapters 2-4)
Requirements: Phys 322 (Electricity and Magnetism II), Phys 325 (Quantum Mechanics II)
Recommended: Phys 431 (Condensed Matter)
Theories of dense nuclear matter with Mia Kumamoto
We will cover the foundations of many-body theory and nuclear interactions. Many-body theory is a rich area of study that has use for nuclear theory, condensed matter theory, and others as well as just being pretty (in my opinion). Nuclear interactions will be understood in the framework of chiral effective field theory, a means to understand interactions of nucleons based on fundamental features of QCD but without as many complications. Applications: nucleon superfluidity at high densities, nucleon-neutrino bremmstrahlung, and others based on time and the student's particular interests.
Reading:
Excerpts from Fetter and Walecka, Quantum Theory of Many-Particle Systems (I think this is an excellent book, but if you don't want to buy it you can borrow mine)
V.G. Soloviev, On the superfluid state of the atomic nucleus, Nuclear Physics, Volume 9, Issue 4, (1958).
R. Machleidt, D.R. Entem, Chiral effective field theory and nuclear forces, Physics Reports, Volume 503, Issue 1, (2011).
Fischer, Tobias. The role of medium modifications for neutrino-pair processes from nucleon-nucleon bremsstrahlung. Impact on the protoneutron star deleptonization. Astronomy & Astrophysics. 593. (2018).
Requirements: Phys 325 (Quantum Mechanics II), Phys 328 (Statistical Physics)