In my last post ‘Constructing spacetime from the quantum tetrahedron: Spacetime as a Bose-Einstein Condensate’ I started to explore how spacetime could be formed as a Bose-Einstein condensate of quantum tetrahedra within the framework of Group Field Theory (GFT).
This week I have been adapting some of the algorithms found in Statistical Mechanics: Algorithms and Computations by Werner Krauth to allow me to begin exploring Spacetime as a Group Field Theory Bose-Einstein Condensate.
First I used a python program to look at how bosons occupy energy levels as the temperature decreases: Basically they all end up occuping the lowest energy level.
The data obtained is plotted in a graph of occupancy number against Energy – notice how the lower energy levels are more highly occupied that the higher ones.
Following this I used a python program with a more sophisticated algorithm to explore how the degree of condensation varies with temperature as used this to produce an animation showing the formation of the Bose-Einstein condensate.
The animation of the data obtained from the python program shows how the Bose-Einstein condensate forms as the temperature is lowered.
(Click picture to see animation)
Given the crudeness of the algorithms I am using so far I think this models an actual Bose-Einstein condensate formation quite well.
- Constructing spacetime from the quatum tetrahedron: Spacetime as a Bose-Einstein Condensate (quantumtetrahedron.wordpress.com)
- [CEA] Dark matter as a Bose – Einstein Condensate: the relativistic non-minimally coupled case (arxiver.wordpress.com)
- Cosmological Constraints on Bose-Einstein-Condensed Scalar Field Dark Matter [CEA] (arxiver.wordpress.com)