Duration 4:1

Phasers locked on target: Phase evolution in the quantum hexagonal billiard

by Nils Berglund

2 684 watched

141

Published 21 May 2021

This simulation shows the same solutions of the Schrödinger equation in a hexagonal domain as the videos /watch/o1GjWRjITW8Ij and /watch/kpl3KVXTGJOT3 but with a different representation. The hue represents the phase (or argument) of the wave function, while the luminosity depends on the modulus squared, giving the probability density of finding the particle at different places. I got the idea from some videos in the playlist /playlist/PLgLEadjw6Qkzd6Z_W1FeWkMvm6cxmPANq and similar suggestions were made by a couple of viewers. The initial state is a Gaussian wave packet with an upward momentum, directed towards the top corner of the hexagon. Music: "Space coast" by Topher Mohr and Alex Elena The simulation solves the Schrödinger equation by discretization. The C code will be published later on https://github.com/nilsberglund-orleans/YouTube-simulations https://www.idpoisson.fr/berglund/software.html Many thanks to my colleague Marco Mancini for helping me to accelerate my code! You may be interested in some science outreach articles: https://images.math.cnrs.fr/_Berglund-Nils-1343_.html

Tags

Probability theory

Stochastic processes

Comments - 42

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@MrPies323 years ago I love how it quickly turns into this undulating cloud of color. 6
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@alecthehuman74573 years ago I love how complex and beautiful these are getting, keep up the quality work: d. 6
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@miguechiesa3 years ago I' ve been expecting this video for so many days! Thanks for considering my suggestion! 3
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@locrogin3 years ago This look fantastic and perfect choice of music for it too. 2
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@ahvavee3 years ago Sometime its just nice to sit and dream and think. Thanks for these. 2
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@yoshi-cs6ib3 years ago Funny thing: when you. Idk how to describe it, but basically you focus your eyes into nothing. When you do that, it appears (partially) white because the red, blue and green mixes. Works best at the beginning. 4
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@ARBB13 years ago Next you could compute bloch functions, they' re quite a treat. 1
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@nonyobisniss79283 years ago These are very beautiful. I' ve been enjoying watching a new one every time you upload something. I did have some questions, which you may have answered i was also interested to know how long your code takes to make a video like this. Is it something that can be achieved in real time on a personal computer? Does the algorithm operate onor some sub-pixel units of space? If so approximately how many? And would the simulation eventually become more and more inaccurate were you to let it run forever?
my final question was: does the pattern ever settle, either into a loop or pretty much random noise?. ...Expand 1
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@sebbes3333 years ago @nils berglund
this might be really hard to simulate( but what happens if the box rotates?
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@ThePositivolp3 years ago The size of the initial wave changes the patterns?
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@emberedison253 years ago Beautiful work.
i tried to change your code to simulate pentagon, but it' s really difficult to do.
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@Alpha13Wolf3 years ago So thats what dmt feels like, the moire you know.
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@diophantine15983 years ago This sort of reminds me of cellular automata.

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Phasers locked on target: Phase evolution in the quantum hexagonal billiard

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Tags

Probability theory

Stochastic processes