Rashid Nazmitdinov: Self-organization of charged particles in circular
geometry and cyclic symmetry

A convenient starting point to treat many-body fermion systems is, in many cases, a mean field description. Self-consistency between the mean field and the single-particle orbitals and total energy minimization are the basic conditions at this level. It may happen that the self-consistent solution breaks one of the symmetries of the original many-body Hamiltonian, a well known phenomenon called spontaneous symmetry breaking. The natural question arises: does such a mean fi eld solution provide a reliable approximation to a real physical state?

We discuss how a symmetry breaking of the Hartree-Fock field leads in circular quantum dots to a specifi c electron localization called a Wigner molecule. At intermediate values of the magnetic field or the Coulomb interaction, the approach to restore the rotational symmetry broken at the mean field, which can be extended for other symmetry breaking cases, will be presented. At strong magnetic field or/and the strong interaction electrons can form, indeed, the classical localization on a few rings, called Quantum Corals. This situation leads us to the problem of self-organization of one-component charged particles, confi ned in a two-dimensional potential with a circular boundary. The basic principles of self-organization of one-component charged particles, confi ned in disk and circular parabolic potentials, are considered, where the circular symmetry is responsible for the self-organization mechanism. We will show how this mechanism provides conditions for a steady formation of a centered hexagonal lattice that smoothly transforms to valence circular rings in the ground state con figurations for particle number n > 180.

© 2021 Department of mathematics, FNSPE, CTU