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Phases and Dynamics of Interacting Quantum Particles
Last Updated: 2026-02-05 16:22:22
Abstract
This course introduces basic models of strongly correlated condensed matter systems. It covers the Hubbard model of strongly correlated metals, the Heisenberg model of quantum magnets, and field theories of Bose liquids and superconductors.Ground state theorems, Kubo formulae, and controlled approximation schemes for the dynamics of strongly correlated quantum phases will be taught.
Objective
This course will teach modern techniques which approach condensed matter systems which are driven by strong interactions. These include quantum spin liquids, transitions between superconductivity and Mott phases of electrons and bosons, and anomalous magnetotransport. The course goes beyond traditional quasiparticle (Fermi–liquid) approximations which are taught in earlier solid state courses.
Content
1. The Hubbard Model. 2. Derivation of Heisenberg and t-J models. 3. Spin wave theory. 4. From negative-U Hubbard model to superconductivity. 5. The Bose Hubbard model, the Higgs mode and granular superconductors 6. Ginzburg-Landau theory and vortex matter.. 7. Flux flow conductivity in superconducting films. 8. Boltzmann theory, Kubo formulas, and continued fraction calculations. 9. Hall and thermal Hall coefficients of metals and insulators.
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- end-of-semester examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Phases and Dynamics of Interacting Quantum Particles |
|
2 h weekly |
| exercise | Phases and Dynamics of Interacting Quantum Particles |
|
1 h weekly |