Background chapter of my thesis.
Introduction chapter of my thesis.
Abstract for my thesis.
Bose$-$Einstein condensation This will be a hand-waiving introduction to Bose-Einstein condensate theory. I’ll begin by introducing what is a Bose-Einstein condensate, followed by how we model it (hint: we use the Gross-Pitaevskii equation). For more detailed derivations, see Pethick and Smith [ISBN: 978-0521846516] or Pitaevskii and Stringari [ISBN: 978-0198507192]. Again, this is another work in progress, so expect me to continually dump my thoughts here and on subsequent posts.
Quantum vortices Consider, if you will, a bucket of water. We can also do this with a closed bottle of water, to prevent from getting wet, but let’s assume we have a bucket. We drop a spoon/stick/paddle in there, and begin to draw a circle, stirring the water. If the item is removed, the water continues to rotate, gradually slowing down before coming to a halt. Let us now assume that the water is spinning quickly, such that a hole develops in the centre.
Time dependent simulations I will focus on the pseudo-spectral Fourier split operator (or split step) method. Firsly, we need to quantised position space by making a grid over a specific range of position values. Assume $-10$ $\mu$m to $+10$ $\mu$m, giving a grid divided into $xDim=2^8$ equispaced elements. Let us call this grid $\mathbf{x}$, and the maximum value $x_\textrm{max}$. The following Julia code will carry out the above: xDim = 2^8; # The resolution of your grid.
Thoughts on permutations of $n$-D data in memory.
Investigating the use of different FFT implementations for quantum dynamics across different hardware architectures
Granted I have not published any of the articles I am writing since my initial post, they are still in the works. Unfortunately, they will also need to wait until my thesis has been written and published (as some of them will be used therein).
As a snapshot, I will intend to discuss the following topics:
However, do not hold your breath for these…
A place for me to place questions I’ve considered, and aim to answer or develop further.