- 10.00 – 10.45: Trial lecture. Title: TBA
- 12.00 – 16.00: Public defence
Ordinary opponents:
- First opponent: Stefano Pittalis, CNR Researcher, National Research Council, Institute of Nanoscience in Modena, Italy
- Second opponent: Sara Giarrusso, Assistant professor, Technical University of Eindhoven, Netherlands
Committee chair: Sølve Selstø, Professor, TKD, OsloMet
Leader of the public defence: Head of Group, Siri Fagernes, Department of Computer Science.
Main supervisor: Andre Laestadius.
Co-supervisors: Marco Matassa and Mihaly Csirik.
Summary
Density functional theory (DFT) is one of the most important tools we have for understanding and predicting the properties of atoms, molecules, and materials. The method is widely used in quantum chemistry, materials science, and condensed-matter physics.
Although DFT is in principle based on an exact reformulation of the ground‑state problem, practical calculations require approximations, which inevitably limit the achievable accuracy. In this thesis, the mathematical and theoretical foundations underlying of two central developments of DFT are investigated.
The first part of the thesis concerns how DFT can be extended to describe systems in which light and matter interact strongly, a field known as quantum-electrodynamical density functional theory (QEDFT). Such systems are becoming increasingly important in modern physics, for example in nanotechnology and quantum optics. Using the mathematical tools of standard DFT, two canonical model systems are analysed, the quantum Rabi model and the multimode Dicke model. These models allow the study of fundamental questions in a controlled setting, and several key theoretical problems can be formulated and solved explicitly in this setting.
The results provide a clear mathematical framework for QEDFT for these systems and demonstrate that DFT techniques can be transferred to simplified models for light-matter interactions.
The second part of the thesis addresses another key problem: How can we determine the effective potential in a Kohn–Sham system given an electron density? This task, known as Kohn–Sham inversion, is crucial for improving our understanding of the relationship between densities and potentials. This connection is fundamental in DFT, where the electron density contains all the information required to reconstruct the potential in the Schrödinger equation that produced it.
In this work, a mathematically rigorous framework based on Moreau–Yosida regularisation is further developed and applied for realistic systems. The framework is applied to representative crystalline materials such as sodium chloride (table salt) and silicon.
The resulting analysis provides the first mathematical error estimates for this class of inversion methods. This enables the controlled computation of the exchange-correlation potential, which may ultimately contribute to the development of more accurate and reliable DFT approximations in practice.
