# Theory

We theoretically study non-equilibrium dynamics of complex quantum systems, focussing on ultra cold gases near 0K temperature, highly excited Rydberg atoms, opto-mechanical devices and hybrid assemblies of these.

Experimentalists can now assemble rather simple building blocks such as atoms, molecules or gas-clouds into ever more complex quantum systems with detailed control. We thus follow nature’s path of creating immense complexity, such as life, out of rather simple ingredients. Re-creating complex systems from nature under well controlled conditions in the laboratory out of e.g. cold atoms is called quantum simulations. This is an idea by Richard Feynman, with which scientists hope to understand systems that are too hard to simulate on our computers, or to get some new ideas that emerge due to the (typically) a lot simpler conditions in the laboratory system.

Our group is interested in discovering ways how the tools above can be turned into quantum simulators for energy transport (e.g. in photosynthesis), or concepts from quantum chemistry (e.g. conical intersections). Beyond that we are also interested in quantum mechanics on mesoscopic scales and numerical solutions of the many-body quantum problem.

We investigate quantum computing with respect applications from science and industry. For more information visit our webpage

1. Quantum Enhanced Technology

- quantum simulators

- quantum enhanced machine learning

- adiabatic vs gate-model algorithms

2. Foundations and Mathematical Methods

- theory of tensor networks

- theory of quantum walks and time symmetry breaking (chiral quantum walks)

- symmetries, invariant theory

3. Frontiers

- applications of information theory to new domains

- mathematics of network theory

- quantum vs stochastic complex systems

- Hamiltonian complexity theory

Algebra - Grops Theory - Representation Theory - Boolean algebra - Graph Theory - Spin Models - Complexity