Quasiclassical theory of quantum dots

Abstract

We review the quasiclassical theory of quantum dots. The starting point of the developed approximate approaches is the observation that in large (in comparison to the effective Bohr radius) quantum dots the energy of the classical Coulomb interactions dominates over the quantum-mechanical kinetic energy. This dominance is further enhanced by application of a perpendicular magnetic field. The classical regime is marked by the formation of structures (the Wigner crystal) and structural transitions. The nature of these phenomena is indeed classical, and they can be successfully tackled using classical approaches which are transparent and easy to understand. In this way heavy calculations typical of quantum-mechanical schemes are avoided and the quantum effects are included in an perturbative manner. We discus, in particular, the application of the renormalized perturbation series to the energy spectra, the structural transitions, the power law behaviour of the critical fields, the global (persistent) and local currents in quantum dots, and dissipation in mixed systems with both quantum and classical degerees of freedom.