Mathematics (Undergraduate)

Weekly classes for Oxford University chemistry undergraduate students.
Course website and lecture materials can be found here (within Oxford)
Sample exam papers can be found here (within Oxford)

Work to be handed in to the PTCL by 5pm on Wednesdays

Numerical Methods for Many-Particle Systems (Graduate)

Held at the Institute for Theoretical Physics, University of Cologne, Germany.
In conjunction with the Bonn-Cologne Graduate School of Physics and Astronomy.

Course Summary

This intensive course is intended to provide both a working understanding and real hands-on experience with the essential numerical techniques of solid state many-body physics.
Rather than a 'black-box' philosophy, the course aims to discuss the theory and physics underpinning numerical approaches. Lectures will introduce models of central importance, such as the Ising model, the Anderson impurity model, the Hubbard model and the Heisenberg model. Using these as concrete examples, the Monte Carlo, Exact Diagonalization, Numerical Renormalization Group and Density Matrix Renormalization Group techniques will be discussed. Students will also gain supervised practical hands-on experience writing, using and modifying simple computer codes to solve real problems.

Visit the 'Numerical Methods' course website

Numerical Renormalization Group (Graduate)

Held at the Department of Theoretical Physics, University of Gothenburg, Sweden.

Course Summary

'Quantum Impurity Problems' are classic paradigms for strong electron correlations in condensed matter physics. They underpin the theoretical description of magnetic impurities in metals, nanodevices such as quantum dots, and appear as effective models within the dynamical mean field theory of correlated materials. Non-perturbative quantum many-body methods must be employed to solve such problems. In this course, we provide the conceptual framework of the Numerical Renormalization Group, discuss technical/practical details of the calculation, and present relevant applications.

Visit the 'Numerical Renormalization Group' course website