Uqs

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.

Investigating the use of different FFT implementations for quantum dynamics across different hardware architectures

GPU enabled Gross-Pitaevskii equation solver

A place for me to place questions I’ve considered, and aim to answer or develop further.