The research in the project aims to give a solid foundation to density functional theory which is a popular method to study the behavior of many-electron systems. In the density functional method the complicated many-particle interactions are replaced by an exact non-interacting system with same electron density. The effective potential in this system is a functional of the density but its form is not known. Finding good approximations has been a long-standing problem and it is therefore of utmost importance to gain new insight in the exact properties of the functional. In a collaboration between physicists and mathematicians this precisely the aim of this work. The approach is based on a discretisation of the many-body problem on finite lattices and is re-formulated in a new mathematical framework involving graph theoretical approaches, which allows for new insights in particular into the topology of density spaces.

2023

2027