Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Condensed Matter Theory 1 (CMT1)

Practical information
Study year 2016/2017
Time
Block 2
Programme level Full Degree Master
ECTS 7,5 ECTS
Course responsible
  • Jens Paaske (6-726363756d674270646b306d7730666d)
  • The Niels Bohr Institute
Course number: NFYK10017U

Course content

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.

Learning outcome

Skills

Participants are expected to learn to:

  1. Describe an interaction quantum mechanical many-particle system by the use of second quantization.
  2. Handle (for example (anti)commuting mixed products of) boson and fermion quantum field operators in various representations (Schrodinger, Heisenberg, and the interaction picture).
  3. Use real-time and Matsubara Green functions to solve interacting many-body problems.
  4. Use mean-field theory to simplify interacting Hamiltonians to simpler manageable problems.
  5. Use equation of motions techniques to obtain Greens functions.
  6. Derive and use Feynman rules for perturbation theory within potential scattering, electron-electron, and electron-phonon interactions.
  7. 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.
  8. 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.
  9. 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.

Recommended prerequisites

Basic knowledge of theory of functions of complex variables is expected.

Remarks

Restricted elective for specialisation "Quantum Physics"

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Education

M.Sc. Physics

Studyboard

Study Board of Physics, Chemistry and Nanoscience

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

C
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Teaching and learning methods

Lectures and exercises

Capacity

No restriction to number of participants

Language

English

Literature

Henrik Bruus and Karsten Flensberg: Many-Body Quantum Theory in condensed Matter Physics", Oxford University Press

Workload

Category Hours
Lectures 28
Practical exercises 28
Exam 24
Preparation 126
English 206

Exam

Type of assessment

Written assignment, 24 timer
24-hour take-home assignment

Marking scale

7-point grading scale

Criteria for exam assessment

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.

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.
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