Frozen waves

Yismuth is my baptism into belief. I have invested most of my summer into understanding Yismuth, spent weeks on calculations that proved ultimately naive, but such striving has nevertheless imbued me with the confidence to calculate. Such sophisticated techniques I have learnt, I begin to see a common structure in many branches of mathematical physics.

The surface of Yismuth is a wonderful playground for the scattering of waves on impurities and step-edges. Incoming and outgoing waves interfere, producing a modulation in the probability density, a frozen wave. Such modulations are a complicated, fluctuating mess when looked upon at short length scales, where scatterings occur across a continuum of momenta and energies. But these fluctuations wash out at longer length scales, where they interfere so effectively as to become invisible. A beautiful pattern emerges from the result of a few scattering events -- they escape this destructive interference by being located at fortuitous curves in the energy-momentum landscape. Such countably few scatterings means we can hope to understand these frozen waves, to predict their shape from models and see them take form under the STM tip.