3 research outputs found
Equivalence of Kinetic Theories of Bose-Einstein Condensation
We discuss the equivalence of two non-equilibrium kinetic theories that
describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a
harmonic trap. The second-order kinetic equations of Walser et al. [PRA 63,
013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum
Boltzmann equation in the low and high temperature limits, respectively. These
kinetic equations can thus describe the system in equilibrium (finite
temperature) as well as in non-equilibrium (real time). We have found this
theory to be equivalent to the non-equilibrium Green's function approach
originally proposed by Kadanoff and Baym and more recently applied to
inhomogeneous trapped systems by M. Imamovi\'c-Tomasovi\'c and A. Griffin
[arXiv:cond-mat/9911402].Comment: REVTeX3, 6 pages, 2 eps figures, published version, minor change
Finite Temperature Models of Bose-Einstein Condensation
The theoretical description of trapped weakly-interacting Bose-Einstein
condensates is characterized by a large number of seemingly very different
approaches which have been developed over the course of time by researchers
with very distinct backgrounds. Newcomers to this field, experimentalists and
young researchers all face a considerable challenge in navigating through the
`maze' of abundant theoretical models, and simple correspondences between
existing approaches are not always very transparent. This Tutorial provides a
generic introduction to such theories, in an attempt to single out common
features and deficiencies of certain `classes of approaches' identified by
their physical content, rather than their particular mathematical
implementation.
This Tutorial is structured in a manner accessible to a non-specialist with a
good working knowledge of quantum mechanics. Although some familiarity with
concepts of quantum field theory would be an advantage, key notions such as the
occupation number representation of second quantization are nonetheless briefly
reviewed. Following a general introduction, the complexity of models is
gradually built up, starting from the basic zero-temperature formalism of the
Gross-Pitaevskii equation. This structure enables readers to probe different
levels of theoretical developments (mean-field, number-conserving and
stochastic) according to their particular needs. In addition to its `training
element', we hope that this Tutorial will prove useful to active researchers in
this field, both in terms of the correspondences made between different
theoretical models, and as a source of reference for existing and developing
finite-temperature theoretical models.Comment: Detailed Review Article on finite temperature theoretical techniques
for studying weakly-interacting atomic Bose-Einstein condensates written at
an elementary level suitable for non-experts in this area (e.g. starting PhD
students). Now includes table of content