20 June, 2026

Notes

2026-10-30

To do!

• quantum mechanics simulations on Julia @mercurio2025quantumtoolbox
• 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 [@horvat2006wigner]
• 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