20 June, 2026

Also available as a slide deck.

To do!

• quantum mechanics simulations on Julia Mercurio et al. (2025)
• finite elements method in julia
• obtaining full surface of section for various \(E_0\)
• fourier transforme of \(x(t), y(t), p_x(t), p_y(t)\)
• simulation of kicked rotor
• changing the orientation and coordinate of the surface of section \(\to\) three dimensional image

Lost Wonderers Thoughts:

I am thinking of what my professor mentioned about states or orbits that are represented in the phase space. Now I am wondering, these are stable orbits, and these appear more pronounced in the quantum mechanical system description and are often known as “quantum scares”. This gets me curious:

• how do phase space representations of chaotic systems look? Maybe look at (Horvat and Prosen 2006)
• how does the higher dimensional geometry/topology compare to quantum wave-functions; here there is a naming conflict: “orbit” and “state” that are used as synonyms i.e. in atomic physics; this lets me wonder about similarities. In particular as the surface of sections look like astoundingly like sections of wave functions

References

Horvat, Martin, and Tomaž Prosen. 2006. Wigner Function Statistics in Classically Chaotic Systems. https://doi.org/10.48550/arXiv.quant-ph/0601165.

Mercurio, Alberto, Yi-Te Huang, Li-Xun Cai, Yueh-Nan Chen, Vincenzo Savona, and Franco Nori. 2025. QuantumToolbox.jl: An Efficient Julia Framework for Simulating Open Quantum Systems. https://doi.org/10.48550/arXiv.2504.21440.