Numerical work using python 1: Bose-Einsten condensation

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.

BE figure 0

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.

BE figure_1

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.

BE fig 4

The animation of the data obtained from the python program shows how the Bose-Einstein condensate forms as the temperature is lowered.

Spacetime as Bose-Einstein condensate v2

(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.

Actual BE condensate formation


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