## Quantum Many-Body Physics

Lecturer: Michael Knap

Teaching Assistant: Alexander Schuckert

**Fall Term**

Lectures: Mon/Wed 10:15-11:45, seminar room 3344

Practicals: Thu 16:00-17:30, seminar room 3344

This course provides a modern introduction to many-body physics. It covers basic theoretical methods and their application to various problems of condensed matter theory, such as the weakly interacting bose gas, interacting electron gas, phonons in solids, quantum magnetism, and superconductivity. Throughout the class relations between experiments and theory will be emphasized. This course will provide students the basic knowledge to follow state-of-the-art research in condensed matter physics and to be able to start their independent research project in that field.

A description of how this course will be graded can be found here.

**Outline:**

**Introduction**

(1.1) Mean-field theory [pdf]

(1.2) Landau theory of phase transitions [pdf]

(1.3) Quantum phases of matter [pdf]

(1.4) Second Quantization [pdf]

**Functional Field Integrals**

(2.1) Feynman's Path Integral in Single-particle QM [pdf]

(2.2) Bosonic and Fermionic Coherent States [pdf]

(2.3) Functional Field Integrals for the Partition Function [pdf]

**Weakly Interacting Bose Gas**

(3.1) Non-interacting bosons [pdf]

(3.2) Weakly interacting bosons [pdf]

(3.3) Consequences of a broken continuous symmetry [pdf]

(3.4) Superfluidity [pdf]

(3.5) Quantum disorder in one dimension [pdf]

(3.6) Thermal disorder and BKT transition [pdf]

**Linear Response Theory**

(4.1) Response functions [pdf]

(4.2) Fluctuation-dissipation relations [pdf]

(4.3) Analytic Properties of Correlation Functions [pdf]

(4.4) Sum rules [pdf]

(4.5) Structure Factor of a Superfluid [pdf]

**Fermi-Liquid Theory**

(5.1) The non-interacting Fermi gas [pdf]

(5.2) The main results of Fermi-Liquid Theory [pdf]

(5.3) Quasi-particle excitations [pdf]

(5.4) Interacting fermion Greens functions and self energy [pdf]

(5.5) Landau's phenomenological approach [pdf]

(5.6) Dynamical properties of a Fermi liquid [pdf]

**The interacting electron gas**

(6.1) Hatree-Fock Approximation [pdf]

(6.2) Coulomb interactions [pdf]

**Superconductivity**

(7.1) The basic phenomenon [pdf]

(7.2) Anderson-Higgs Mechanism [pdf]

(7.3) Flux quantization and vortices in superconductors [pdf]

(7.4) BCS theory from functional field integrals [pdf]

(7.5) Microscopic derivation of the Ginzburg-Landau theory [pdf]

**Tutorials**

Problem Set 1 [pdf]

Problem Set 2 [pdf]

Problem Set 3 [pdf]

Problem Set 4 [pdf]

**List of Presentations** [pdf]

Topics are assigned on a first-come first-serve basis.