- Eric Roon, University of Arizona
- Ergodic Quantum Processes in Finite von Neumann algebras
- 04/11/2023
- 10:30 AM - 11:20 AM
- C304 Wells Hall
- Brent Nelson (banelson@msu.edu)
In 1997, H. Hennion used a non-standard metric to show a kind of multiplicative ergodic theorem for the convergence of an infinite product of positive random matrices. Recently Movassagh and Schenker proved a quantum-channel version of Hennion's ergodic theorem. We will discuss the necessary background to understand the generalization of Hennion's metric to the state space of a tracial von Neumann algebra $(M,\tau)$, and a characterization of contraction mappings in this metric. We will discuss generalizations of the theorems of Movassagh and Schenker to everywhere-defined, positive maps on the noncommutative $L^1$ space. Time permitting, we will sketch the proof of our characterization of contraction mappings and discuss its applications to locally normal states on the spin chain. This is part of work in progress in collaboration with Brent Nelson.
