SCDFT · Strictly-correlated Density Functional Theory: methodology development and application to semiconductor nanostructures and ultracold atom gases

This project has two main objectives: First, to further develop and generalize the formalism of strictly-correlated Density Functional Theory (SC DFT), which is ideally suited for the study of strongly-interacting systems. Second, to apply it to the study of both semiconductor nanostructures and ultracold atom gases. This novel methodology was recently proposed by the head scientist of the project and co-workers and, despite being still in its early stage, it has already shown an enormous potential and very promising preliminary results. We will first further develop the formalism, generalizing it for a broader range of problems (for example, for non-spherically-symmetric systems), improving the accuracy and validity of the initially proposed functionals, and constructing more efficient algorithms for the involved numerical calculations. Particular emphasis will be put on the ""hybrid KS-SC DFT"" approach, consisting in implementing some of the tools of SC DFT into the Kohn-Sham framework, and whose first pilot calculations have given rise to very potentially relevant results, allowing for first time for the construction of a Kohn-Sham functional able to capture the features of the strongly-interacting limit. Also, we will apply the methodology to strongly-correlated semiconductor nanostructures, studying, e.g., Wigner-localization-related phenomena that have recently been observed in experiments. SC DFT will allow us to study particle-number regimes where other approaches fail to be accurate (e.g., Kohn-Sham DFT) or computationally feasible (e.g., Configuration Interaction). Finally, we will try to generalize the formalism for its application to ultracold atom gases, and in particular to the very timely case of dipolar systems. Our aim is to further investigate symmetry-breaking and Wigner-localization effects that have recently been observed in dipolar gases in the few-body limit as a function of the orientation of the dipoles.""