Complex dynamics in planar two-electron quantum dots

Quantum dots play an important role in a wide range of recent experimental and technological developments. In particular they are promising candidates for realisations of quantum bits and further applications in quantum information theory. The harmonically confined Hooke s atom model is experimentally verified. In order to study effects of an anharmonic confinement potential on spectral properties of planar two-electron quantum dots a sophisticated numerical approach is developed. Classical and quantum features of complexity and chaos are investigated. The concept of offset entanglement, the entanglement of harmonic models in the non-interacting limit, is introduced. It shows that only in the groundstate the electrons are not entangled in the fermionic sense. The applicability, validity, and origin of Hund s first rule in general quantum dot models is further addressed. In fact Hund s first rule is only applicable, and in this case also valid, for one pair of singlet and triplet states in Hooke s atom. For more realistic models of two-electron quantum dots an extension of Hund s first rule for unnatural parity states, the alternating rule, is found to be valid.