Bose-Einstein condensation of interacting particles and the quantum de Finetti
theorem
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The observation of Bose-Einstein condensation in dilute atomic gases twenty
years ago has given a new impetus to the theoretical study of large bosonic
systems. Much of our current understanding of this physics is based on the
mean-field approximation, which in this context roughly amounts to assuming that
all particles behave independently of one another. That this approximation is a
sensible one for a great variety of large bosonic systems is a remarkable fact,
and I will argue that it can be seen as following from a very special structure
property of the set of bosonic states, the quantum de Finetti theorem. I shall
discuss the original theorem along with recent variants and applications to
interacting bosonic systems. This is joint work with Mathieu Lewin and Phan
Thành Nam.