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Mathematical Andreev billiards

Mathematical Andreev reflection is retro-reflection with parity. By this, we mean that when a pointmass intersects a portion of a billiard table not obeying the standard Law of Reflection, the pointmass returns upon the incoming path.

In addition to this, the ball is assigned a parity and such parity changes with each intersection with said side. The side for which the billiard ball experiences Andreev reflection is call the Andreev subset of the billiard table boundary. We begin building a mathematical foundation for dynamics in an Andreev billiard table, as it is discussed within the context of physics. To such end, we have begun simulating billiard trajectories in a 2D rectangular billiard table with the base of the billiard table being the Andreev subset. Andreev reflection, as it is discussed above, is meant to ideally model the dynamics of an electron in a nanowire lying on a superconductor plate. Elementary results in mathematical billiards are quickly applied to classify dynamics in such a model. We also perturb the boundary of the 2D model so as to introduce explanations for observed behavior not fitting existing models for electron-hole dynamics in a nanowire.