Quantum dots: few-body, low-dimensional systems

Quantum dots are examples of nanostructures which are attracting much interest in the fields of both pure and applied physics. The smallest dots currently being fabricated contain N<10 interacting electrons and have an effective dimensionality d<or=3. The measurement and interpretation of the energy spectra associated with such few-particle quantum dots represents a considerable experimental and theoretical challenge. The single-electron confinement energy, the cyclotron energy for moderate magnetic fields and the electron-electron interaction energy can be of similar magnitude and may therefore be equally important in determining the few electron energy levels. In addition the energy spectrum is likely to be strongly N dependent for such small N. Here we review the results to date for few-particle quantum dots (N<10). We discuss the extent to which theoretical predictions emerging from detailed numerical calculations can be reproduced using analytically solvable microscopic models, and the extent to which both are consistent with recent experimental results.