NFYK10017U Condensed Matter Theory 1 (CMT1)
This course is an introduction to quantum field theoretical
methods aimed for both experimentalists and theorists with
particular focus on condensed matter physics. The content spans a
wide range of topics necessary for understanding concepts and
methods used in advanced solid state physics. Finally, the course
provides a good foundation for the course CMT2 and for doing active
research in condensed matter physics at the Niels Bohr
Institute.
In the course, we focus on the interacting electron gas,
describing metals and semiconductors, and use this as an example to
illustrate the techniques taught. The course is meant to teach
the fundamental filed-theoretical concepts and techniques such as
second quantization, equations of motion for operators,
many-particle Green functions at finite temperatures, and Feynman
diagrams.
Skills
Participants are expected to learn to:
- Describe an interaction quantum mechanical many-particle system by the use of second quantization.
- Handle (for example (anti)commuting mixed products of) boson and fermion quantum field operators in various representations (Schrodinger, Heisenberg, and the interaction picture).
- Use real-time and Matsubara Green functions to solve interacting many-body problems.
- Use mean-field theory to simplify interacting Hamiltonians to simpler manageable problems.
- Use equation of motions techniques to obtain Greens functions.
- Derive and use Feynman rules for perturbation theory within potential scattering, electron-electron, and electron-phonon interactions.
- Perform a detailed calculation and regularization of the ground state energy for the interacting electron gas including the screening of long-range Coulomb interactions and its Landau damped plasmons.
- Describe single-particle excitations in an interacting many-particle system in terms of renormalized quasi-particles. This includes being able to obtain effective masse and charge, Fermi surfaces, Z-factors and lifetimes.
- To use all these acquired skills to solve relevant physics problems, including mainly issues within the physics of solid materials, nano-scopic systems, quantum liquids and ultracold atomic gasses.
Knowledge
In the course, we focus on the interacting electron gas, describing
metals and semiconductors, and use this as an example to illustrate
the techniques taught. The course is meant to teach the fundamental
filed-theoretical concepts and techniques such as second
quantization, equations of motion for operators, many-particle
Green functions at finite temperatures, and Feynman
diagrams.
Competences
This course will provide the students with the required background
for further studies within this research field, i.e. the course
CMT2 or a master thesis. The course will provide most of the modern
formalism used in the scientific literature on condensed matter
physics.
Henrik Bruus and Karsten Flensberg: Many-Body Quantum Theory in condensed Matter Physics", Oxford University Press
- Category
- Hours
- Exam
- 24
- Lectures
- 28
- Practical exercises
- 28
- Preparation
- 126
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Written assignment, 24 timer24-hour take-home assignment
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
More internal examiners
- Re-exam
- The re-examination will be held as an oral examination with a duration of 30 minutes and no preparation time if 10 or less students are registered for the re-examination.
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.
Course information
- Language
- English
- Course code
- NFYK10017U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C (Mon 13-17 + Wednes 8-17)
- Course capacity
- No restriction to number of participants
- Continuing and further education
- Study board
- Study Board of Physics, Chemistry and Nanoscience
Contracting department
- The Niels Bohr Institute
Course responsibles
- Jens Paaske (6-726363756d674270646b306d7730666d)