A quantitative understanding of bonding in condensed matter systems demands a solution of the many electron problem. This course will show how the many electron problem can be mapped onto single electron problems in an approximate way using the Hartree and Hartree Fock approximations and a formally exact way using (density functional theory and the Kohn Sham equations. Further, some of the methodology used to solve the Kohn Sham equations in complex systems will be described. In the last part of the lectures, some extensions and examples will be analysed, and we will critically evaluate the strength and weaknesses of DFT and other ab-initio electronic structure methods.
Niels is a professor of theoretical physics at the University of Manchester. His research interests are in the theory of condensed matter and nuclear physics, combining computational and theoretical approaches, using many-body and ab initio techniques. He has a special interest in twistronics and higher-order topological materials. Outside physics, he works as associate Dean for Teaching and Learning in the Faculty of Science and Engineering.
Statistical Mechanics aims to provide a macroscopic description of a physical system starting from knowledge of its microscopic properties. The methodology and techniques are widely used throughout condensed matter physics and are also today being applied to understand the dynamics of model ecologies, economies and societies. In these lectures, we will revisit the equilibrium properties of matter – such as phase transitions and universality – from the perspective of dynamics (as opposed to statics, as is typically done in undergraduate courses). Then we will examine successively further-from-equilibrium systems, ending with a discussion of fluctuations in driven systems, a subject currently generating considerable excitement in this field.
Richard Blythe is a Professor of Complex Systems at the University of Edinburgh. Since his PhD days, he has been researching models and theories for nonequilibrium dynamical systems. Applications of these models include transport in biological systems, traffic flow, population dynamics and language change.
This course deals mainly with the influence of interactions on the electrons in materials. We begin with a review of second quantisation and the Fermi gas theory of metals, and then progress to Landau’s Fermi liquid theory and the notion of quasiparticles. The effect of impurities on the Fermi liquid (including the Kondo effect) is discussed, and we then move on to consider how the Fermi liquid gives way to other phases as the interactions are increased, concentrating on the Stoner instability and the Mott insulator. We analyse the magnetism in the Mott insulating phase, developing the concept of spin waves. Finally, we make a survey of some experimental data on strongly correlated crystalline solids, giving basic interpretations in terms of the concepts developed in the course.
Chris is a reader at the University of St Andrews. He works on various topics in the theory of strong correlations, including non-Fermi-liquids, highly frustrated magnets, non-equilibrium atomic fluids, and vortex-mediated phase transitions.