Characterization of Non-Equilibrium Properties of Solid State Devices

Recent years has seen rapid growth in our understanding of non-equilibrium quantum mechanics. This has led to the prediction and experimental realization of many exciting phenomena. Most striking are non-equilibrium phase transitions like recent experimental evidence of light induced superconductivity, which could have far-reaching applications in electronic devices. Despite this recent progress in non-equlibrium quantum mechanics is mostly limited to specific areas such as periodically driven systems (Floquet theory) and even in this area remain many challenges. Examples of challenges are a lack of understanding at low driving frequencies about what happens to bands the case of 2 bands is well understood but for more bands our current understanding is limited. This is an especially pressing matter in the context of the ever-growing zoo of moire materials such as twisted bilayer graphene. One goal of this work is to apply existing Floquet theory techniques to these materials and develop new methods that are easier applicable to multiband systems in the low frequency regime. Another interesting topic are systems subjected to sudden changes so called quenches. Interesting here is what meta-stable quantum states can be achieved and their potential electronic applications. It is also important to understand how stable systems are against quenches. This is especially important in the context of quantum computing where the stability of states is the main limiting factor for reliable computations. Current theoretical tools face many limitations such as small systems sizes and short times. Therefore, a second goal of this work is to study the effect of quantum quenches in the context of the Kitaev honeycomb model (this has applications in quantum computing), improve upon the current theoretical limitations and find other potential applications in electronic devices. In summary, the goal of this work is the application of existing non-equilibrium computational tools to moire materials as well as systems relevant to quantum computing such as the Kitaev honeycomb model and the subsequent development of new tools for interesting regimes.