Speaker: Alexander Pechen
Affiliation: Princeton University
Title: Non-crossing pair partitions and free number process in the low density limit.
Time and Place: Wednesday, November 28, 2:00-2:55pm, Milner 317.
Abstract: In this talk I will discuss the appearance of non-crossing pair partitions and of a free number process in the analysis of the dynamics of open quantum systems in the low density limit. The low density limit is a formal theoretical description of the kinetic regime of evolution of quantum open systems interacting with dilute quantum gases. The main result to be presented is that truncated correlation functions, taken with respect to a Gaussian gauge invariant state, of generalized boson number type operators describing such systems converge in the limit to correlation functions of a free number process and that for these truncated correlation functions only diagrams associated to non-crossing pair partitions survive in the limit while all the others go to zero.
This result shows the appearance of a free number process in the analysis of a class of physical systems and makes a connection between quantum open systems and free probability.
The talk is based on the work J. Math. Phys. 47 (2006) 033507.