Enhanced dynamical symmetries and quantum degeneracies in mesoscopic quantum dots: Role of the symmetries of closed classical orbits

We present an analysis of a class of theoretical models important to the study of mesoscopic effects in quantum dots, that reveals a new example of a fundamental principle: the existence of classical paths having a lower symmetry than the system Hamiltonian leads to accidental degeneracies in the corresponding quantum-mechanical spectrum, even in the case where the Hamiltonian is non-integrable. We also show that these degeneracies form a fractal structure with an associated "Devil's staircase" that can be observed using present experimental techniques.