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

¹ Department of Physics and Astronomy, Western Washington University Bellingham, WA, 98225, USA
² Department of Physics, Simon Fraser University Burnaby, British Columbia, Canada V5A 1S6

Received: 22 July 1999
Accepted: 19 June 2000

Abstract

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.