Dr Matt Buican Project Abstracts
BSc Project Abstracts
Emergent Phenomena in Statistical Physics and Quantum Field Theory
In theoretical physics, we often start with simple rules that govern how a system behaves microscopically. From these simple rules, many interesting and subtle phenomena appear when we study the system macroscopically. To get a handle on these macroscopic descriptions, physicists use the framework of the renormalization group (RG). The main point of this project will be to get a solid grounding in the RG as well as the associated phenomena of universality and criticality.
In theoretical physics, we often start with simple rules that govern how a system behaves microscopically. From these simple rules, many interesting and subtle phenomena appear when we study the system macroscopically. To get a handle on these macroscopic descriptions, physicists use the framework of the renormalization group (RG). The main point of this project will be to get a solid grounding in the RG as well as the associated phenomena of universality and criticality.
We will start by studying these concepts in the context of equilibrium statistical physics (an excellent reference for this part of the project is John Cardy’s book, “Scaling and Renormalization in Statistical Physics”). Using these ideas, we will explore the emergent behavior of various interesting systems both numerically and analytically. Time permitting, we will use this intuitive grounding and move on to study (in a somewhat unorthodox way) some of these ideas in the context of quantum field theory.
Anyonic Chains
The first part of this project focuses on constructing the Hilbert spaces of anyonic chains (these are certain generalizations of usual spin chains). In the second part of the project, we will take the thermodynamic limit of these systems and study the resulting phases. In particular, we will see how conformal theories naturally emerge in this simple setting.
The first part of this project focuses on constructing the Hilbert spaces of anyonic chains (these are certain generalizations of usual spin chains). In the second part of the project, we will take the thermodynamic limit of these systems and study the resulting phases. In particular, we will see how conformal theories naturally emerge in this simple setting.
MSci Research/Investigative Project Abstracts
Emergent Phenomena in Statistical Physics and Quantum Field Theory
In theoretical physics, we often start with simple rules that govern how a system behaves microscopically. From these simple rules, many interesting and subtle phenomena appear when we study the system macroscopically. To get a handle on these macroscopic descriptions, physicists use the framework of the renormalization group (RG). The main point of this project will be to get a solid grounding in the RG as well as the associated phenomena of universality and criticality.
In theoretical physics, we often start with simple rules that govern how a system behaves microscopically. From these simple rules, many interesting and subtle phenomena appear when we study the system macroscopically. To get a handle on these macroscopic descriptions, physicists use the framework of the renormalization group (RG). The main point of this project will be to get a solid grounding in the RG as well as the associated phenomena of universality and criticality.
We will start by studying these concepts in the context of equilibrium statistical physics (an excellent reference for this part of the project is John Cardy’s book, “Scaling and Renormalization in Statistical Physics”). Using these ideas, we will explore the emergent behavior of various interesting systems numerically and analytically. Time permitting, we will use this intuitive grounding and move on to study (in a somewhat unorthodox way) some of these ideas in the context of quantum field theory (QFT). In particular, we will discuss partition functions and the operator product expansion in three-dimensional QFT. Moreover, we will study how to constrain the emergent macroscopic behavior of certain very simple three-dimensional QFTs using these tools, and we will learn what it means to count degrees of freedom in QFT. For the particularly motivated student, this work may lead to genuinely new results.
Anyonic Chains
The first part of this project focuses on constructing the Hilbert spaces of anyonic chains (these are certain generalizations of usual spin chains). In the second part of the project, we will take the thermodynamic limit of these systems and study the resulting phases. In particular, we will see how conformal theories naturally emerge in this simple setting.
The first part of this project focuses on constructing the Hilbert spaces of anyonic chains (these are certain generalizations of usual spin chains). In the second part of the project, we will take the thermodynamic limit of these systems and study the resulting phases. In particular, we will see how conformal theories naturally emerge in this simple setting.
