This is some stuff related to my undergrad thesis in physics at Washington State University. It's not my best work and I don't think it has any applications, outside of being a somewhat-interesting artifact of mathematics and physics.
In this thesis, we arbitrarily calculate the Lyapunov exponent of BECs modeled by the Gross-Pitaevskii equation. The exponent is found using the
The Gross-Pitaevskii equation (GPE) is a nonlinear Schrödinger equation used in modeling Bose-Einstein condensates (BECs).
Using Lyapunov exponents, chaos was characterized in the GPE in the one-dimensional case.
The GPE was simulated using Python using finite-difference methods in space and an adaptive Runge-Kutta solver was used to evolve the equation in time.
When an initial state of the GPE with positive coupling constant is perturbed, positive Lyapunov exponents were found.
There was a proportionality found between positive Lyapunov exponents and the nonlinear coupling constant of the GPE,
- My undergraduate thesis (pdf)
- GPE IPython notebook (scratch-work)
- Lorenz IPython notebook (scratch-work)
- I'm not actually sure if these were the notebooks that I used for the paper, or just some scratch work for generating plots for the report.
- I dislike the LaTeX template we were using. I've looked at the templates of other schools and thought ours was very lackluster.
- This was conducted before I had my classes in QM. So, I feel like there was a lot of this thesis that I didn't truly understand. As a result, I didn't enjoy working on this report, thought it didn't engage me, and overall disliked the topic.