Time: 16:45-18:15

Location: Moonstone Building / Ground Floor / Seminar Room F

Attendees of the seminar are invited to join us for socializing at the Heuriger after the talks!

ISTA Speaker: Joscha Henheik

Title: Speed limits in quantum systems 

Abstract: In their 1972 seminal paper, Lieb and Robinson proved that information in locally interacting quantum lattice systems can only spread with a finite speed. Hence, their celebrated Lieb-Robinson bound (LRB) formalizes the existence of an effective „light cone“ for the many-body quantum dynamics. Despite being long forgotten, LRBs experienced a great revival in the beginning of the century, as it proved to have several important applications. 

In this talk, I will explain a prototypical LRB and discuss a few modern utilizations.

VSM Speaker:  Adam Lindström (University of Vienna)

Title: Decoupling a system of PDE's using perturbation theory. A key to uncoupled Dirac-Yang-Mills fields. 

Abstract: We will start by describing the Dirac-Yang-Mills system on a closed Riemannian manifold. This is a coupled system of elliptic PDE’s involving connections on and sections of vector bundles over the base manifold. It has its origins in physics where, posed on a spacetime, it constitutes a generalization of Maxwells equations and describes the interaction between fermions (such as electrons or quarks) and a force field (such as the electromagnetic force or the strong force).

The Dirac-Yang-Mills system are the Euler-Lagrange equations of the Dirac-Yang-Mills action functional. However, this is unbounded in both directions, making proving existence of critical points challenging. In this talk we will therefore present a result which in many cases allows for the Dirac-Yang-Mills system to be decoupled into a pair of equations, the Yang-Mills and the Dirac equation, which are significantly easier to treat and which are separately well-studied in the closed Riemannian setting. We will describe how analytic perturbation theory gives an elegant characterization of this phenomenon.