## Mid-Term Report Summary - SEED (Seizing Electron Energies and Dynamics: a seed for the future)

Electronic correlation causes a wide range of interesting phenomena, such as superconductivity. It strongly impacts our surroundings – think about the creation of defects in a material or tissue that can be caused by a radiation field: it is often induced by the correlated motion of many electrons. In the animal world, the adhesion of a gecko on a surface is supported by quantum fluctuations of the electrons. Many other examples touch technological applications, such as solar cells. Although the underlying Coulomb interaction is « simple » and well understood, a unifying framework is still missing that would allow us to describe, analyze, understand and predict all those phenomena on the same footing. The aim of this project is to introduce and establish a completely new method for the calculation of properties of correlated electron systems.

Most often, the complex problem of electronic correlation is approached by supposing that one of the ingredients is small, for example, the interaction. This allows one to start from a much simpler problem, for example, a system with no interaction. However, interesting systems and situations are often those where this hypothesis fails.

Our approach is completely different. It is based on the idea to explore the response of a system to an external perturbation, in order to learn something about the system itself. Mathematically, this is obtained by an approximate solution of a multidimensional functional differential equation. The exact solution of the full equation cannot be found, but mathematical techniques coupled to physical insight allow us to design better and better solutions.

In this way one equation, which takes only one line of formula, leads to new understanding of the electronic excitation of oxides, predictions of the results of difficult experiments that have yet to be performed, ideas for the design of new materials for solar cells, or insight concerning the limits of validity of widely used theoretical approaches.

Most often, the complex problem of electronic correlation is approached by supposing that one of the ingredients is small, for example, the interaction. This allows one to start from a much simpler problem, for example, a system with no interaction. However, interesting systems and situations are often those where this hypothesis fails.

Our approach is completely different. It is based on the idea to explore the response of a system to an external perturbation, in order to learn something about the system itself. Mathematically, this is obtained by an approximate solution of a multidimensional functional differential equation. The exact solution of the full equation cannot be found, but mathematical techniques coupled to physical insight allow us to design better and better solutions.

In this way one equation, which takes only one line of formula, leads to new understanding of the electronic excitation of oxides, predictions of the results of difficult experiments that have yet to be performed, ideas for the design of new materials for solar cells, or insight concerning the limits of validity of widely used theoretical approaches.