Confined quantum systems: a study of ground state and collective excitations

Abstract

This thesis is devoted to the study of ground state and collective properties of a class of mesoscopic systems - quantum confined systems. In quantum confined systems the particles (bosons and fermions) are artificially confined within a small volume by applying electrostatic potential or magnetic field. This thesis consists of 2 parts. The ground state and collective excitations in an interacting systems of bosons confined in a trap are discussed in part 1; The Bose-Einstein condensation of dilute atomic vapour in a magnetic trap is considered. The ground state properties of condensate in a harmonic oscillator trap is discussed semiclassically, and also within variational approach. A systematic semi classical expansion to calculate the thermodynamic properties of a system of bosons confined in any arbitrary trap is developed. This method is applied to various physical systems, and in particular applied to calculate the thermodynamic potential analytically of a weakly interacting Bose-gas confined in three dimensional harmonic oscillator potential. Part 2 deals with the systems of electrons(fermions), confined in a two dimensional trap, the quantum dot system. Part 2 analyses the electronic structure and collective excitations of a confined two dimensional electron system at zero temperature within semi classical density functional formalism. A simple solvable model of quantum dot with logarithmic two body interaction is presented and its quantum mechanical energy levels are calculated. The collective excitations in a quantum dot containing finite number of electrons is studied. The excitation energies of multi-pole modes and breathing mode of a dot at zero magnetic field is estimated with the use of the energy weighted sum rule method. The dependence of the collective excitation energies on the system size and other external parameters is studied. The collective magneto plasmon excitations in a quantum dot with finite number of electrons at high magnetic field limit are investigated.