Near absolute zero, a gas of quantum particles can condense into an
unusual state of matter, called Bose-Einstein condensation, that
behaves like a giant quantum particle. I will discuss results that
provide the rigorous connection between the physics of the microscopic
dynamics and the mathematics of the macroscopic model, the cubic
nonlinear Schrodinger equation (NLS). In joint work with Benjamin
Schlein and Gigliola Staffilani, we have handled two-dimensional
Bose-Einstein condensation—and the periodic case is especially
interesting, because of techniques from analytic number theory and
applications to quantum computing. Time permitting I'll also mention
work in progress on large deviations for quantum many-body systems,
and phase transitions for the invariant measures of the NLS.
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