GROUP THEORY CLASSIFICATION SCHEMES OF THE N-ELECTRON QUANTUM DOT

Abstract

We develop a general framework for discussing collective behavior in confined many-electron systems. Our specific goal is the application to N-electron quantum dots, which are mesoscopic semiconductor systems of great current interest as possible ultra-small electronic devices. In view of its broad applicability, we are able to cast the discussion of the many-electron problem in general terms. We consider the general N-interacting particle system in d dimensions and study its bilinear dynamical symmetry group which is the noncompact symplectic group Sp(2Nd, R). Giving their explicit dependence on N and d, we focus on the classification of many-particle bound states which requires knowledge of the unitary discrete series representation theory of Sp(2Nd, R) and the corresponding character reductions. We also discuss matrix elements of the generators, the implementation of the Pauli principle, and a procedure to derive total angular momentum quantum numbers associated with a given total spin.