Mathematical and Numerical Methods for Complex Quantum Systems

Bose Einstein condensation, the nonlinear Schrodinger equation, and a central limit theorem

Kay Kirkpatrick

University of Illinois at Urbana-Champaign

Near absolute zero, a gas of quantum particles can condense into an unusual state of matter, called Bose-Einstein condensation (BEC), that behaves like a giant quantum particle. The rigorous connection has recently been made between the physics of the microscopic many-body dynamics and the mathematics of the macroscopic model, the cubic nonlinear Schrodinger equation (NLS). I'll discuss recent progress with Gerard Ben Arous and Benjamin Schlein on a central limit theorem for the quantum many-body dynamics, a step towards large deviations for Bose-Einstein condensation.