Mathematics Colloquium — Special Lecture
Spring 2010
Kay Kirkpatrick
NYU, Courant Institute
Bose-Einstein condensation: from many quantum particles to a quantum "super-particle"
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.