Аннотация:

One of the important achievements of modern technology consists in creation of «artificial atoms» or quantum dots, where a finite number of electrons is confined electrostatically in a nanometer sized region. In the framework of the approach, developed by the authors, it is shown that the external magnetic field gives rise to the hidden symmetries of two-electron quantum dots. These symmetries manifest themselves at the transition from the chaotic to the regular motion. At these transitions the new integrals of motion are found, that are alike to the Runge-Lenz vector.

The importance of various symmetries is shown as well for:

1. the author’s prediction of shell structure of quantum dots, that was discovered experimentally;
2. size quantization effects that explain the experimental behavior of the singlet-triplet transitions of quantum dots in the external magnetic field;
3. the resolution of the issue of the localized states creation (Wigner molecule) in the circular symmetric quantum dots;
4. the quantum entanglement behavior in two-electron quantum dots in the external magnetic field;
5. the ballistic transport of electrons through quantum dots (quantum billiards) of different shapes.

(В связи с выдвижением на премию ОИЯИ)