The GPE is a mean field equation that has been incredibly successful in describing the dynamics of Bose Einstein condensates (BECs). The equation features a non-linear term and thus allows for stable soliton solutions in 1D and additional topological defects such as vortices in 2D. The goal of this project is to study these phenomena using the split-step Fourier method.
We provide three configurable models:
In order to run the scripts, copy the files to a newly created project directory and simply use
$ python <model_name>Here, replace model_name by either solitons1d, solitons2d, or vortices2d.
For more detailed information on the configurations and the models themselves, have a look at the project report and the comments within the scripts.
Have a look at the project report for theoretical background and a detailed analysis.
The line-structure of the solitons breaks down to single-quantized vortex-antivortex pairs.
Vortices and anti-vortices arranged on a perfect regular lattice exhibit stable periodic cycles.
When the vortex positions are slightly disturbed they decay to lower-quantized vortices.
References:
- Sebastian Erne Diplomarbeit
- M. Karl and T. Gasenzer New. J. Phys. 19:093014 (2017)