Aims
- To provide an introduction to and generate interest in
modern condensed matter physics, studying a few topics in depth.
- To illustrate the concept of
spontaneous broken symmetry in
quantum systems, with special focus on the theory of superfluids &
superconductors
- To use systems of current research interest to illustrate the
theoretical concepts
- To provide a microscopic theory of neutral superfluids,
as applied to Bose condensates and superfluid helium
- To highlight the role of phase coherence
in neutral superfluids
- To provide a quantum theory of the excitations in a Bose
fluid, emphasising its connection to the phenomenon of superfluidity
- To provide a phenomenological theory of phase
coherence in superconductors,
in order to explain the signature phenomena of superconductivity:
- Meissner effect (magnetic flux expulsion)
- Flux quantisation
- Josephson effect
- To explain the microscopic origin of Cooper pairs
in superconductors
- To describe the Bardeen-Cooper-Schrieffer
microscopic theory of superconductivity
- To introduce techniques in quantum field theory:
- second quantisation
- vacuum fluctuations
- number-phase representation
Learning Outcomes
At the end of the course, the students will be able to:
- describe qualitatively the role of interactions in many-body systems
- describe qualitatively the concept of spontaneous broken symmetry
- describe qualitatively the basic phenomena of superfluids and
superconductors: zero resistance, Meissner effect, flux quantization and
Josephson effect.
- give simple examples of neutral superfluids, e.g. Bose condensates
- give simple examples of applications of superconductivity
- explain the distinction between a superconductor and a perfect conductor
- describe the distinction between type I and type II superconductors
in terms of their behaviour in a magnetic field
- describe the phenomenological Ginzburg-Landau theory of phase coherence
- use the Ginzburg-Landau theory of phase coherence to explain
basic phenenemona in superfluids and superconductors
- understand the concept of second quantisation and the role of
of creation and annihilation operators in this context
- understand and calculate the zero-point fluctuations of
simple many-particle systems, eg one-dimensional quantum solid
- derive a second-quantised description of Bose fluids in terms
of density and phase fluctuations, and calculate the degree of
Bose-Einstein condensate in an interacting system
- describe qualitatively the mechanism of phonon-mediated electron
attraction in metals
- discuss quantitatively the pairing instability for two electrons
at the Fermi surface
- describe the basic framework of the Bardeen-Cooper-Schrieffer
(BCS) theory of superconductors: ground state wavefunction and excited states