Exploring Topological Invariants of Quantum Systems in Julia | Volker Karle | JuliaCon 2023

This talk explores the capabilities of the Julia ecosystem for topological physics, specifically the calculation of topological invariants for periodically driven non-equilibrium Quantum systems. Often, these quantities are related to topological properties of complicated geometric objects. Julia's ability to streamline these calculations and easily integrate mathematical libraries via multiple dispatch offers a powerful toolbox that simplify the exploration of new phenomena considerably.

In my current research, I focus on the evaluation of non-Abelian topological invariants in periodically driven non-equilibrium quantum systems. These invariants offer a rich phenomenology and can give rise to new and unexpected dynamic behavior in current-day experiments. They are related to the properties of quasi-energy manifolds that form knots in space and time. However, their calculation can be very challenging and computationally demanding.

To address these challenges, I have been utilizing the Julia ecosystem, which offers a powerful toolset for numerical calculations. Julia's ability to easily integrate mathematical libraries and perform multiple dispatch has enabled me to streamline the calculation of these topological invariants.

In summary, my research aims to utilize the Julia ecosystem to evaluate non-Abelian topological invariants numerically, with the goal of gaining a deeper understanding of the exotic material properties they give rise to. The results of this research have the potential to lead to new insights and applications in the field of quantum physics.

Time Stamps:
00:00 Welcome!
00:10 Help us add time stamps or captions to this video! See the description for details.