Theoretically analysing first principle models of disordered quantum systems, such as quantum dots or quantum wires, is extremely challenging and often impossible. However, most macroscopically observable emergent phenomena, e.g. electric conductivity, are universal. They do not depend on microscopic details. Together with two PhD students and three postdocs, we will make use of this fact by investigating and classifying such phenomena within more accessible coarse-grained random matrix models.

We will study transport properties of disordered quantum systems, such as quantum dots and quantum wires, modelling the system components by random matrices. The simplest instance of such a model is the quantum dot, which does not have an internal structure. We recently analysed this model in 'Scattering in quantum dots via noncommutative rational functions'.

The problem of describing the diffusion of a quantum particle in a disordered environment is connected to deep mathematical conjectures such as the BGS-quantum chaos conjecture, the extended states conjecture by Fyodorov-Mirlin and the conjectured metal-insulator phase transition of the Anderson-model. Some of these have been open for half a century. The main challenge is to understand the metallic or delocalised phase of the system. We will study random band matrices, a heuristic model for quantum diffusion, for which major breakthroughs have been achived in recent years.