Monday, November 27, 2017 at 4:15pm to 5:15pm
Kay Kirkpatrick (Illinois)
"Two Quantum Central Limit Theorems"
We will discuss a quantum central limit theorem in the context of Bose-Einstein condensation (BEC), a special phase of matter near absolute zero in which a gas of quantum particles can condense and behave as if it were a single giant quantum particle. This work also makes the rigorous connection between the physics of the microscopic many-body dynamics and the mathematics of the macroscopic PDEs often used as reduced descriptions of BEC.
We will also discuss a central limit theorem for generators of quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. There is also a connection to free Araki-Woods factors. (Joint work with Gerard Ben Arous, Michael Brannan, Benjamin Schlein, and Gigliola Staffilani.)