Finite Temperature Models of Bose-Einstein Condensation

Abstract

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.

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 contents

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Cited by in corpus (5)

• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach
• Cold atoms in double-well optical lattices
• PGPE theory of finite temperature collective modes for a trapped Bose gas
• Regulating atomic imbalance in double-well lattices