July 2nd, 2011

beartato phd

(no subject)

Over lunch I thought up an (n+1)-dimensional (that is, n spatial dimensions, one time) analogue of my little (1+1)-dimensional toy system from before. In it there are (n+1) particle states per spatial position, each one of which takes a step towards a vertex of the n-simplex, and turns into a superposition of the (n+1) states that looks like a row from the DFT matrix of the appropriate dimension. The unitarity of the DFT means unitarity of the overall transform (with motion in space) comes pretty much for free.

I threw together a javascript+canvas animation of the (2+1)-dimensional system. Sadly, it is not isotropic, but it still looks pretty. Click anywhere on the canvas to stop or start computation.