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Quantum Lissajou Scars

In this crude 2D visualization, I am trying to depict the inner tri-dipole and the personality layer of the electron. I’m just learning the mathematican animation language Manim. It looks like Manim has a 3D library so I need to check that out. Eventually I hope to make short educational videos to show the math and the visualization together.

Imagine, a system with three orbiting electrino:positrino point charge dipoles each at different frequency, energy, and radius of orbit and creating amazing electromagnetic wave fronts. I just found this visualization of the emergence from systems with two orbits of different frequencies and tracking the sin() of the radius vector. Wow, this kinda blows my mind. It akin to a wave equation generator. Does the math of Lissajous figures or a related dynamical geometry factor into the standard model?

Interestingly, the arXiv search with both lissajous and quantum in the abstract returned only one paper . Here is the arXiv link. https://arxiv.org/abs/1911.09729.

Check out this abstract! I haven’t read the paper yet, but the abstract is exactly what I would expect – a strong mapping between classical and quantum. Perhaps the tri-dipole Noether core is generating these Lissajous scars.

Quantum Lissajous Scars
J. Keski-Rahkonen, A. Ruhanen, E. J. Heller, and E. Räsänen
Phys. Rev. Lett. 123, 214101 – Published 21 November 2019

“A quantum scar—an enhancement of a quantum probability density in the vicinity of a classical periodic orbit—is a fundamental phenomenon connecting quantum and classical mechanics. Here we demonstrate that some of the eigenstates of the perturbed two-dimensional anisotropic (elliptic) harmonic oscillator are strongly scarred by the Lissajous orbits of the unperturbed classical counterpart. In particular, we show that the occurrence and geometry of these quantum Lissajous scars are connected to the anisotropy of the harmonic confinement, but unlike the classical Lissajous orbits the scars survive under a small perturbation of the potential. This Lissajous scarring is caused by the combined effect of the quantum (near) degeneracies in the unperturbed system and the localized character of the perturbation. Furthermore, we discuss experimental schemes to observe this perturbation-induced scarring.”

The authors are variously affiliated with :

  • Computational Physics Laboratory, Tampere University, Finland
  • Department of Physics, Harvard University, Cambridge, MA

Well, the paper is encoded in language that is difficult for me to grok at this point, but still I think there may be a mapping to this work. I wrote a letter to one of the authors. Perhaps they may respond.

I won’t get distracted by Lissajous figures, but it is important to keep my eyes open for mappings between the point charge model and the standard model, because that will be important evidence.

Systems of harmonic oscillators are quite important in physics. I am searching for the optimal mathematical methods to use to describe systems of point charges parsimoniously. Even simple things like whether to use x,y,z,t coordinates or r, theta, phi could make a lot of difference in formulating the math. At a more sophisticate level, how might I keep track of electric field objects emitted continuously and spherically by each point charge, and the intersection of the resulting wavefronts with all point charges they encounter? That is essentially what is need to compute the action in each discrete time step of a simulation.

For those of you unfamiliar with Fourier series, here are a couple of great videos from Grant Sanderson’s 3Blue1Brown channel that explain the mathematics and then show how a Fourier series can model any curve.

Now, let your mind imagine a universe where every stable particle, including particles of spacetime aether, is constructed from structures containing 1 to 3 three orbiting dipoles acting as harmonic oscillators, each with a frequency range from 0 to the Planck frequency, less any unstable combinations of course.

J Mark Morris : Boston : Massachusetts

By J Mark Morris

I am imagining and reverse engineering a model of nature and sharing my journey via social media. Join me! I would love to have collaborators in this open effort. To support this research please donate: https://www.paypal.me/johnmarkmorris

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