These are the slides from Michaelmas 2022. If you want a nice printable version for saving as a PDF, you can use e.g. austen.uk/lectures/many-body-wavefunctions/?print-pdf#/
If you ever want access to the $\LaTeX$ for the mathematical expressions, right click and select Show Math As > TeX Commands
Interested in theoretical condensed matter research?
Summer internships are available at the Max Planck Institute for the Physics of Complex Systems in Dresden
Lectures
- Take place in the Small Lecture Theatre at the Cavendish Laboratory from 09.30-11.00 on Tuesdays and Thursdays.
Synopsis
Many Body Wavefunctions
Product States. Fermi gas. Density, density matrix, and pair distribution.
Quantum Hall Effect
Landau levels. Laughlin wavefunction. Fractional charge, Fractional statistics.
The Elastic Chain
Quantizing a chain. Ground state displacement fluctuations. statistics.
Spin Models
Heisenberg model. Heisenberg chain. Magnons. Antiferromagnets. Symmetry breaking. Spin wave theory.
A is for Annihilation
Product states and occupation numbers. Creation and annihilation operators. The case of fermions. Representation of operators.
B is for Bunching
Density correlations. Hanbury Brown and Twiss effect. Hartree–Fock theory.
Lattice Models
Tight binding models. Hubbard models and the Mott transition. Superexchange.
Bose Gas
Gross–Pitaevskii approximation. Superfluidity. Bogoliubov theory.
Fermi Gas
Interactions described by perturbation theory. Quasiparticles. Landau Fermi liquid.
Superconductivity
Cooper’s problem. BCS theory. The BCS-BEC crossover.
Response and Correlation
Response functions. Structure factor. Dielectric function. Sum rules.
Course materials
Some books that you may find useful
- Advanced Quantum Mechanics - A Practical Guide, Nazarov and Danon
- Introduction to Many-Body Physics, Coleman
- Interacting Electrons and Quantum Magnetism, Assa Auerbach
Past exam papers (with solutions)
Discuss
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