Lecturer:
Associate professor John Ove Fjærestad (office: E5-126, email: john.fjaerestad@ntnu.no, phone: 93448)
Contents:
Occupation number representation for nonrelativistic fermionic and bosonic many-particle systems. Interacting electron gas. Lattice models for fermions and spins. Spin-wave theory of ferro- and antiferromagnets. Symmetries and conserved quantities. Broken symmetries, Goldstone modes. Green functions. Matsubara formalism. Many-particle perturbation theory and Feynman diagrams. Various applications. Relativistic quantum mechanics: The Klein-Gordon and Dirac equations.
Lectures:
Thursday 12:15-14:00 and Friday 12:15-13:00 in E5-103.
Tutorials:
Friday 13:15-14:00 in E5-103 (starting in week 3).
As a pre-exam requirement, each student will present solutions to one or more tutorial problems
at at least one tutorial (more details will be provided later).
Quality assurance:
Information about the education quality assurance system
Exam:
Tuesday 19 May, 9:00-13:00.
You may bring:
- an approved calculator
- Rottmann: Matematisk formelsamling/Mathematische Formelsammlung
- Barnett and Cronin: Mathematical Formulae for Engineering and Science Students
Pre-exam Q&A session:
Friday 15 May at 14:30 in R21.
Curriculum:
The curriculum ("pensum") for the exam is based on the material that has been covered in lectures, plus the written solutions to the tutorial problems. For the lecture material one may alternatively use the following notes/sources:
- Second quantization
- Second quantization representation for the Hamiltonian of an interacting electron gas
- Noninteracting electrons. The free electron gas
- Tight-binding model for electrons in a crystal
- The Hubbard and Heisenberg models, spin-wave theory of ferro- and antiferromagnets, broken symmetry and Goldstone modes
- Transformations and symmetries in quantum mechanics
- Introduction to Green functions and many-body perturbation theory (except Sec. 4.10)
- The Klein-Gordon equation: Sec. 17.1.1 in Hemmer's "Kvantemekanikk".
- The Dirac equation: Sec. 17.2 in Hemmer.
Note that the following topics which were discussed in lectures (some of them only briefly) are not examinable:
- the material on Bloch and Wannier states discussed before the tight-binding model
(but note that the material on the tight-binding model is examinable, cf. notes above)
- the detailed derivation (using projection operators) of the S=1/2 Heisenberg antiferromagnetic model from the
half-filled Hubbard model in the strong-interaction limit
- the Mermin-Wagner theorem
- aspects of broken symmetry that are not covered in Sec. 6 of the magnetism notes (but, to be clear, the material in that section is examinable)
- calculating the conductivity from the Kubo formula (Sec. 4.10 in the Green function notes)
- graphene and its tight-binding dispersion
In the tutorials, the following topics are not exam relevant:
- problem 1 in Tutorial 4
- issues related to the projection operators P in problem (e) in
Tutorial 5.
Resources:
Main resources:
- Notes by the lecturer.
- Ch. 17 on relativistic wave equations in "Kvantemekanikk" by P. C. Hemmer (Tapir, 2005).
Supporting resources:
There is (probably) no single textbook that covers all the material that will be discussed in the course. Some books that may be useful include
- Bruus and Flensberg, "Many-body quantum theory in condensed matter physics" (Oxford, 2004)
- Altland and Simons, "Condensed matter field theory" (2nd ed., Cambridge, 2010)
- Fetter and Walecka, "Quantum theory of many-particle systems" (Dover, 2003) (from 1971)
- Auerbach, "Interacting electrons and quantum magnetism" (Springer, 1994)
- Doniach and Sondheimer, "Green's functions for solid state physicists" (World Scientific, 1998)
- Jishi, "Feynman diagram techniques in condensed matter physics" (Cambridge, 2013)
- Khomskii, "Basic aspects of the quantum theory of solids: Order and elementary excitations" (Cambridge, 2010)
Other references may be added later.
Tutorial sets:
| Tutorial | Date | Presenter | Problems | Solution |
|---|---|---|---|---|
| 1 | 16 Jan | Krohg, Fredrik Nicolai | |
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| 2 | 23 Jan | Hugdal, Henning Goa | |
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| 3 | 30 Jan | Amundsen, Morten | |
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| 4 | 6 Feb | Børkja, Mathieu Le Boulvais Chirac, Theophile Jean Marie |
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| 5 | 13 Feb | Folkestad, Sarai Dery Grøver, Sigurd Loe |
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| 6 | 20 Feb | Gunnarsen, Gudmund Hveding Hunvik, Kristoffer William |
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| 7 | 27 Feb | Klausen, Håkon Strand Kjønstad, Eirik Fadum |
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| 8 | 6 Mar | Indrehus, Sunniva Kleiven, David |
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| 9 | 13 Mar | Pfänder, Lukas Schanner, Maximilian Arthus |
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| 10 | 20 Mar | Sanchez Garcia, Alfredo Ignacio Sánchez Navas, Sergio |
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| 11 | 27 Mar | Grønli, Thomas Seim, Eivind |
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| 12 | 10 Apr | Toresen, Martin Alexander Vethaak, Tom |
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| 13 | 17 Apr | Leinaas, Jan Erik Aarøen, Ola |
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Other:
Past exams
2014 course website
2014 exam, solution sketch