# TQM Lectures 2022

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

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## 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.

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2021

2022

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