A. A. Belov

Electron clusters in a quadratic potential

Abstract Clusters of electrons in a quadratic external potential are studied. By expanding in inverse powers of the space dimensionality the ground state energy of the N -electron cluster is found in the whole range of variation of the problems parameter. The rearrangement of electron orbitals in the crossover region is investigated.

Lamb shift of Rydberg atoms in a resonator

The Lamb shift of a Rydberg atom in a cavity is shown to be enhanced with the resonance interaction of a virtual atomic transition and cavity modes. The dependence of the Lamb shift on quantum numbers and atomic number changes drastically. By shifting cavity walls and scanning the atomic beam one can vary the Lamb shift. The value of the Lamb shift in a cavity may exceed a typical magnitude of the fine-structure energy. For a rough resonance tuning the Coulomb multiplet is strongly mixed and a novel classification is necessary.

Gapless edge excitations in the fractional quantum Hall effect and conformal invariance

We propose the conformal-invariant model for the description of the edge excitations (EE) in the FQH states using field-theoretical construction with current-current interactions. We discuss the classification of the topological orders (TO) of a given model. Using Chern-Simons ~ Wess-Zumino equivalence, we determine the possible types of the excitations in the FQHE — namely, we calculate their charges and statistics.