Triaxial Ellipsoidal Quantum Billiards

Quantum Monodromy in Prolate Ellipsoidal Billiards

This is the third in a series of three papers on quantum billiards with elliptic and ellipsoidal boundaries. In the present paper we show that the integrable billiard inside a prolate ellipsoid has an isolated singular point in its bifurcation diagram and, therefore, exhibits classical and quantum monodromy. We derive the monodromy matrix from the requirement of smoothness for the action variab...

Quantum Billiards

Classification of symmetric periodic trajectories in ellipsoidal billiards.

We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R(n+1) without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2(2n)(2(n+1)-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R(2)) ...

Integrable ellipsoidal billiards with separable potentials, billiards on quadrics, and the Poncelet theorem

One of the best known discrete integrable systems is the billiard inside an n-dimensional ellipsoid. Veselov showed that generic complex invariant manifolds of the algebraic billiard map are open subsets of (coverings of) hyperelliptic Jacobians and that the restriction of the map to such manifolds is described by the shift by a constant vector (an algebraic addition law). Later, Dragovic and R...

Ellipsoidal InAs Quantum Dots

Uses of semiconductor quantum dots (QDs) have been explored for attractive applications such as quantum information processing, lasers and solar cells to name a few. However, their ability to become integrated with existing technologies depends on shape, composition and size, all of which play a role in modifying both the optical and electrical properties of the QDs. However, an in-depth unders...