QM1: Quantum many-body physics

SM0 Module title:   Quantum many-body physics (QM1)
Module convenor:   Dr. Rob Smith (Birmingham)

The aim of this module is to introduce the basic ideas and techniques of quantum many-body physics, and to apply them to some important condensed matter systems. The main formalism used is that of second quantization, in which particle creation and annhilation operators are introduced in order to avoid dealing directly with wavefunctions. Second quantization will be developed in some detail in the first lecture, and applied to various systems in the subsequent lectures. Since models for condensed matter systems are usually written as second quantized Hamiltonians, it is important to be able to "read" such a Hamiltonian to understand the physics involved.

Syllabus: (Tentative)
  • Second quantization and occupation number representation.
  • Bogoliubov theory for repulsive bosons: superfluidity.
  • BCS theory for attractive fermions: superconductivity.
  • Time-dependent perturbation theory. Fermi's golden rule. Berry's phase.
  • Transport Applications: Tunneling; Scaling Theory of Localization

Assessment: will be in the form of a completed problem sheet to be handed-in at the end of the course. The deadline is February 29th, 2008. Hand-in your solutions by this date to Dr. R. Smith (if in Birmingham), Dr. J.P. Garrahan (if in Nottingham), or Dr. D. Leadley (if in Warwick).

2 hours
13/11/2007 - 11:00