QM Research Seminar: From the sampling of quantum dynamics via coherent semiclassical analysis to quantum emulation.

In this talk, we address a keystone problem in quantum foundations: the systematic factorisation of S-matrices. We develop an approach based on a subtle mix of geometric and Berezin-Toeplitz quantization. Within this framework, we demonstrate how the Stokes phenomenon—arising in the semiclassical analysis of Schrödinger equations in coherent-state representations—provides a natural mechanism of approximate factorisation of S-matrices into discrete products. After discussing conditions for these product decompositions to be finite, we argue that this procedure offers a novel framework for quantum emulation. This is joint work with Steven Rayan, and the manuscript is currently in preparation.