CLASSIFICATION OF N-ELECTRON STATES IN A QUANTUM-DOT

The physical symmetries of an N-electron gas in a d-dimensional quantum dot are studied. The symplectic group framework is used to discuss the dynamical modes of the system and to classify the N-electron states including spin. We focus on the results for a few-electron (N less-than-or-equal-to 12) dot in d = 2 dimensions. For N < 4 electrons the types of configurations appearing are strongly N dependent. The allowed configurations for N < 4 are also highly restricted compared to those for N greater-than-or-equal-to 4. These findings suggest that results of few-electron (N < 4) cluster calculations may have limited applicability to large-N systems.