Nonlocal correlations in nonequilibrium: parquet equations

In the search for materials with new functionalities -- needed for photovoltaics, spintronics, energy storage -- a thorough undestanding of the behaviour of electrons is crucial. As charged particles, electrons interact with one another through Coulomb interaction. In many cases, despite strong Coulomb repulsion, the electrons can still be viewed as independent particles. In some materials, however, the interaction makes electrons strongly correlated, leading to phenomena that are not easily understood in terms of isolated particles -- they are called emergent -- such as magnetism or superconductivity. In nonequilibirium, when additional energy is added to the system for example by shining light on it with a laser, new emergent phenomena occur. We even speak of novel, emergent, states of matter -- e.g. photoinduced superconductors. These nonequilibrium states of mattter are usually present for limited, usually short, time. Studying them we however learn not only what interesting states can be created but also about properties of materials that in equilibrium stay hidden and are not detectable in equilibrium experiments. This knowledge can then be used to engineer materials with properties on demand in the future. Understanding electronic systems out of equilibrium requires adequate theoretical modeling in order to make full use of their properties. Particularly the study of emergent new states or even new quasiparticles often requires computation of two-particle correlation functions, which is already a formidable task for equilibrium systems. The computational techniques are however constantly improving and it is becoming feasible to apply quantum field theory methods to computation of correlation functions for nonequilibrium systems. In the project I will formulate and apply a diagrammatic method already well established in equilibrium -- the parquet equations method -- to study nonequilibrium electronic systems. On the example of model systems that are still computationally feasible, I will investigate how the emergent phenomena in nonequilibrium come about. The methods I propose will also allow me to analyze which components or properties of a system are necessary for a given phenomenon to occur and which work against it. This knowledge will bring us closer to engineering materials on demand.