Admission requirements
Quantum Theory, Statistical Physics a.
Recommended: Statistical Physics b and Effective Field Theory.
Description
The course gives an introduction into the theory describing the emergence of macroscopic matter from interacting microscopic constituents.
This revolves around the explanation of emergence principles such as spontaneous symmetry breaking and long range order, adiabatic continuity, collective excitations such as Goldstone bosons, quasiparticles, and topological excitations, as they arise both in weakly- and strongly interacting systems.
We will explain the mathematical theories underlying the understanding of the following states of matter:
The crystal, including the theory of quantum elasticity describing phonons and phonon interactions.
Magnetism, with a focus on Mott-insulators and superexchange, spin-wave theory.
Spin- and charge density waves in the weak coupling limit: the concept of nesting.
The microscopic theory of superconductivity and superfluidity: from local pairs to the Bardeen-Cooper-Schrieffer theory.
The Ginzburg-Landau effective field theory of macroscopic superconductivity.
The Fermi-liquid including the origin of quasi-electrons, zero sound and plasmons.
With the help of the second quantization approach, perturbation theory and the mean-field theory the course introduces a number of fundamental concepts such as long-range order, spontaneous symmetry breaking, elementary, collective and topological excitations. These general concepts are illustrated on a range of archetypal examples such as crystalline solids, magnets superfluids and superconductors and Fermi-liquid metals.,
Course objectives
The course will provide students with an exercise ground to apply the mathematical techniques of quantum many body theory. This includes the second quantization formalism, Green's functions/propagators, linear response theory, perturbation theory, mean field theory, quantum statistical physics and elementary applications of the path-integral formalism.
Upon completion of this course you will be able to:
Construct second-quantized models of quantum many-body systems
Calculate thermodynamic properties of model systems
Calculate linear response functions (e.g. magnetic susceptibility) of model systems
Describe elementary excitations of a model system
Use perturbation theory in a many-body system
Apply mean-field theory to interacting systems of bosons and fermions
Construct topological excitations of a quantum fluid
Use the random phase approximation
Derive and solve the BSC equation for the superconducting gap
Compute the pole strength and effective mass of Fermi-liquid quasiparticles.
Schedule
The timetables are available through My Timetable (see the button in the upper right corner).
Teaching method
See Brightspace
Assesment method
The final grade will be determined as follows:
Homework assignments (40%)
Final exam (60%)
Resit, review & feedback
Examinations are held twice during the academic year for each component offered in that academic year. Midterm tests cannot be retaken. The Board of Examiners determines the manner of resit for practical assignments.
For review and feedback, see Brightspace.
Reading list
A set of lecture notes prepared by the lecturer.
Background reading (not mandatory):
P.Phillips, "Advanced solid state physics" (Cambridge Univ. Press, 2012).
A. Altland and B. Simons, "Condensed matter field theory" (Cambridge Univ. Press, 2010)
P. Coleman, "Introduction to many body physics" (Cambridge Univ. Press, 2016)
P. Nozieres and D. Pines, "Theory of Quantum Liquids"(Avalon publishing, 1999)
Registration
Enrolment through MyStudyMap (button in upper right corner) is mandatory. General information about course and exam enrolment is available on the website.
Contact
For substantive questions, contact the lecturer(s) (listed in the right information bar).
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.