01299nas a2200097   4500008004300000245006000043210005900103520097400162100002901136856003601165       2007                        en_Ud  00aReduced density matrices and Bose-Einstein condensation0 aReduced density matrices and BoseEinstein condensation3 aEmergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the level of marginals.\\nThe topic of correlations in the condensed state is addressed in order to show their influence at this level of marginals, both in the true condensed state and in the suitable trial functions one introduces to approximate the many-body structure and energy. Complete condensation is shown to be equivalently defined at any fixed k-body level, both for pure and mixed states. Further, it is proven to be equivalent to some other characterizations in terms of asymptotic factorization of the many-body state, which are currently present in the literature.1 aMichelangeli, Alessandro  uhttp://hdl.handle.net/1963/1986