I felt like it a little overdue to describe what my job is this summer, but here goes.

This year was the first time, almost ever, that I’ve had an over-supply of job offers which are actually legitimate. The feeling was awesome – I felt like a real person, and I highly suggest it. All three job offers were NSERC (Natural Sciences and Engineering Research Council) USRAs (Undergraduate Student Research Awards), which I get paid about $6800 over the summer for, depending on how rich your department is. The job offers (in order of how good they were) were:

1. Quantum Phases and Semi-definite Programming in Math Department at Queen’s
2. Ethanol Accounting in Portable Electronics at the Fuel Cell Research Centre
3. Mathematical Physics in Materials for the Materials Dept. at Queen’s

I rejected number 3 for number 2, and then number 2 for number one, as that’s the order I received them in. I’m not regretting my choice at all, as its turning out to be way more interesting than I expected. My “interview” consisted of me sitting in my supervisor’s office for an hour while he explained the project to me, after which I was sold. Disadvantages of the other jobs:

– Project boring/not well-defined
– People not as enthusiastic/present

I geuss this is because the projects I rejected were sort of made “for” me, as I was going around asking for them, whereas the research I’m working on has a strong establishment in the department. While you would think that would make it boring, there is actually lots of development as it is a relatively new field.

So what am I actually doing?

Here’s our webpage, which has a description.

The motivation for the project is to gain a better understanding of high-temperature superconductivity, and generally for all “quantum phases” in a solid lattice (e.g. ferromagnetic, etc.). Superconductivity is a state in which a material has no resistance to electricity, which traditionally occurs at only very low temperatures, usually below 20 K (Kelvin). Expanding superconductivity to a more reasonable temperature has all sorts of useful application, as no energy loss occurs, no heat is produced, and current will flow forever in superconductive circuits. High-temperature superconductivity, which has been produced in the lab at temperatures up to 130 K, is generally still unknown as it is not explained under the same theory as conventional superconductors. Curiously, all high-temperature superconductors found to date have had a two-dimensional lattice structure, meaning that they conduct poorly in one dimension, and perfectly in the other two.

Science does have method to describe the behaviour of electrons (or any particle) called the Schrodinger Wave Equation, but this is too computationally intensive to solve for almost any useful problem, despite its high accuracy. I actually remember that Richard Feynman mentioned this for atomic nuclei (as the equation applies to protons and neutrons) in one of his lectures, which I own on CD.

This leads to the reason this research is associated with Math Department and not the Physics Department, as we are working on an algorithm which is fast and less intensive, while still being shown to compare very closely (like 4 decimals) to Schrodinger Equation results. This method is called Semidefinite Programming, a very fresh technique (for the world of math) and is based on the Pauli Principle, meaning simply that two electrons of the same spin cannot occupy the same position in a lattice. This reduces the problem to onlyvery large (~800 x 800) matrices which need to be minimized according to certain constraints, which is a typical semidefinite programming problem. The minimum matrix will represent the ground state of the electron distribution, meaning the lowest energy level. An investigation of what this is represents will determine where the electrons are and how they are moving – if they are in Cooper Pairs, then we are looking at superconductivity.

Where the dimensionality comes in (remember that high-temperature superconductors only operate in two dimensions?) is the simulations to come. So far, the Master’s was done on a ring, representing one-dimension. Hopefully by the end of the summer we will refine our algorithms enough to go up to two dimensions by using a torus, followed by a hypertorus for three dimensions. Then, dimensionality can be compared.

So what am I doing right now? Writing this entry. The last few weeks I’ve been proving some theorems to myself and doing alot of reading to catch up to the speed of my supervisors. I’m also working with one other student (Ben) which is a plus compared to the other jobs, as working alone last summer drove me crazy! I’ve also written some useful algorithms which are already being used to investigate old data. And as its a research job, I’m generally slacking off most of the time and relaxing, which tends to be the best attitude to inspire creativity and learning.