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≤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≥4. These findings suggest that results of few-electron (N<4) cluster calculations may have limited applicability to large-N systems.