NFYK10003U Condensed Matter Theory 2 (CMT2)
The aim of the course is to provide the student with an overview
of modern topics in quantum condensed matter systems, including
broken symmetry in quantum phases (superconductivity) and
renormalization group, and to familiarize them with more advanced
methods. The course uses both the operator version of many-body
physics taught in Condensed Matter Theory 1, and the functional
path integral methods, which will be introduced in the course. In
addition, the course highlights some concept of topology applied to
physical systems relevant for the research areas currently covered
The microscopic origin of superconductivity is developed starting with the description of coupled electron-phonon systems and to make a link between the operator and path integral methods this is done in both ways. Then the renormalization group method is introduced and applied to various physical systems, for example ferromagnetic transitions, dissipative quantum tunneling, quantum impurity problems, and the Kosterlitz-Thouless transition.
Participants are expected to learn to:
- Explain the mechanism behind formation of a superconducting condensate
- Use mean-field theory in fermionic many-body systems using both the operator and functional integral methods.
- Apply the principle of renormalization group theory on quantum simple systems.
- Read and explain to others modern theoretical literature in condensed matter physics
After the course, the student will understand the formulation of many-body physics in the language of coherent state path integrals and will be able to apply this to physical models for systems with broken symmetry, e.g. ferromagnetic transitions. The microscopic origin of superconductivity and the description of coupled electron-phonon systems will also be known. Furthermore, the student is familiar with the key elements of renormalization group applied to condensed matter systems, dissipative quantum tunneling, quantum impurity problems, and the Kosterlitz-Thouless transition.
This course will provide the students with a competent background for further studies within this research field, i.e. a M.Sc. project in theoretical condenses matter physics, and it will provide the students with mathematical tools that have application in range of fields within and beyond physics.
1. "Condensed matter field theory", second edition, by
A. Altland og B. Simons.
2. Lecture notes.
- 7,5 ECTS
- Type of assessment
- Oral examination, 20 minContinuous assessmentThe evaluation has two components: (a) a 30 minute presentation of a research paper in front of the class (25%), and (2) a 20 minute oral exam without time for preparation (75%).
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
More internal examiners
- Oral exam, 20 minutes, 7 point grading scale, internal censorship counts for 75% of the final grade. Points from the presentation done during the course (if any) counts for the remaining 25%.
Criteria for exam assesment
Grade 12 is given for the independent and convincing achievement, documenting deep knowledge and insight on all aspects of the course goals. Grade 2 is given for the just acceptable achievement.
- Theory exercises
- Project work