Please Note: From 20. January 1998 I have started working at the Institute of Electronic Structure and Laser at the Foundation of Research and Technology Hellas (FO.R.T.H.), located in Heraklion, Crete, Greece. In early May 1998, I am expected to start the 20-month compulsory military service in Greece, serving in the air force. At this point it is still uncertain whether I will be able to continue my scientific research at the FO.R.T.H. institute during that time.
Abstract of DPhil Thesis (227 Pages, incl. diagrams, figures and references)
This thesis presents a novel microscopic approach for the study of both static and dynamical aspects of trapped dilute atomic Bose-Einstein condensates at temperatures below the transition point. The approach presented here is a generalised mean field one. It is based on a coupled equations of motion formalism for the condensate mean field and fluctuations around it, and suitable decoupling approximations. The derived equations extend beyond the conventional mean field treatments (known as Hartree-Fock-Bogoliubov, HFB) by including more complex anomalous averages of the Bose field operators. This enables the examination of the validity of conventional theories. A separation of timescales argument is given which justifies the perturbative treatment of the anomalous averages in suitable limits. This leads to the rigorous introduction of effective interatomic potentials (ladder diagrams) in the interactions between condensed and excited atoms, thus avoiding the usual misapplication of the pseudopotential approximation. The nonlinear Schr\"{o}dinger equation for condensate evolution at finite temperatures is determined in the limit of weak interactions. The modifications imposed on this equation due to the presence of the medium (mean field) are analysed. Such treatment shows the use of a quasiparticle (HFB) basis to be rather limited, and a consistent approach necessitates a consideration of quasiparticle interactions. A simple self-consistent theory including such interactions is developed for the study of the elementary excitation spectrum of trapped Bose-Einstein condensates. This is based on a suitably generalised effective interaction which is both position and temperature-dependent. Explicit results are given for 1-dimensional condensates. Finally, the dynamical aspects of Bose condensation are further investigated by studying the evolution of excited atoms. A generalisation to the coupled dynamics of both condensed and excited atoms is outlined.
To obtain a copy of this thesis, please email myself or any other member of the Oxford BEC group.
Electronic mail address:
Oxford: proukaki@mildred.physics.ox.ac.uk
Heraklion: nick@iesl.forth.gr
Permanent Home Address (Greece)
56 Ploutarchou street, Politia, Athens 146 71, GREECE
Tel: + 30 - 1 - 6207 259 or 6207 248