Residual interactions in many particle systems lead to strong correlations. A multitude of spectacular phenomenae in many particle systems are connected to correlation effects in such systems, e.g. pairing, superconductivity, superfluidity, Bose-Einstein condensation etc. Here we focus on few-body bound states in a many-body surrounding.

1. – Introduction 1. 1. Why BEC?. – In the month we began writing this paper, fourteen papers on the explicit topic of Bose-Einstein condensation (BEC) in a dilute gas appeared in the pages of Physical Review. Both theoretical and experimental activity in BEC has expanded dramatically in the three years since the first observation of BEC in a dilute atomic gas. One is tempted to ask, why? Why i...

Quantized vortices is a well-know signature of superfluidity. They have been studied extensively in superfluid Helium, type-II superconductors, Bose Einstein condensates and more recently in Fermi gas. We will discuss some mathematical analysis and numerical simulations of the quantized vortex nucleations in superconductors and Bose-Einstein condensates and discuss their connections and similar...