Just before the beginning of my fourth year of graduate school, I found an excellent thesis project to do under the "advision" of Dr. Gary Williams. This was a great relief, because I had exhausted the possibilities for my plans A through D and was unsure how Gary would respond to my proposal. He accepted me as a student, and I worked with him to further flesh out his theory of the superfluid phase transition.
Here is a quick explanation of my dissertation research. There is a working theory, or mathematical procedure, that is used to calculate thermodynamic properties of superfluid helium and properties associated with the phase transition between normal fluid and superfluid. However, it's abstract, giving little physical insight, and it's cumbersome and difficult to work with. Dr. Gary Williams' theory utilizes an assumption about the physics of this process (that the vortex loops are more important than the spin waves) to drastically simplify the mathematics and calculate more properties more easily. His theory provides evidence for what is the physical mechanism behind the phase transition and so illuminates what is really physically happening. It also provides a way to simplify analysis by only considering larger "renormalized" vortex loops. Furthermore, the lessons learned with superfluid helium indicate that we can understand high-temperature superconductors in the same way, and if this is true there may be some immediate practical use for this theory by applying it to high-temperature superconductors. In fact, this model may also provide insight for models of cosmic strings and phase transitions of the early universe after the big bang, when the universe was rapidly cooling. My main topic in this research is to examine the properties of superfluid helium 1) in equilibrium at different pressures, and 2) in a rapid, non-equilibrium cooling (quench), and to compare my results with some superfluid experiments and simulations that have been done.
Here are some interesting related links:
- Superfluid (Wikipedia)
- Dr. Gary Williams (my advisor)