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Condensed Matter Theory 1 - PhD course
Provider: Faculty of Science

Activity no.: 5908-20-11-31 
Enrollment deadline: 31/07/2020
Date and timeNovember 2020 - January 2021
Regular seats20
ECTS credits7.50
Contact personJulie Meier Hansen    E-mail address: juliemh@nbi.ku.dk
Enrolment Handling/Course OrganiserMark Spencer Rudner    E-mail address: rudner@nbi.ku.dk
Semester/BlockBlock 2
Scheme groupC
Exam requirements3 homework assignments must be submitted and approved in order to take the exam.
Exam formWritten assignment
Exam formAndet/Other
Exam detailsWritten assignment, 3 days 24-hour take-home assignment
Grading scale7 point grading scale
Exam re-examination Same as the regular exam. If a student has not fulfilled the prerequisite for the exam during the course, homework assignments can be (re-)submitted until 3 weeks before the re-exam.
Course workload
Course workload categoryHours
Lectures28.00
Practical exercises28.00
Exam24.00
Preparation126.00

Sum206.00


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 field-theoretical concepts and techniques such as second quantization, equations of motion for operators, many-particle Green functions at finite temperatures, and Feynman diagrams.

Formel requirements
Important information for students outside of Denmark:
To apply for participation in this course, it is required that you send an email to the course organizer with your information and motivation for joining the course. Do not use the online application. Thank you.

Learning outcome
Skills

Participants are expected to learn to:

•Describe an interacting 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, 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 field-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.

Literature
See Absalon for final course material. The following is an example of expected course literature.

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

Teaching and learning methods
Lectures and exercises

Remarks

 

Important information for students outside of Denmark:
To apply for participation in this course, it is required that you send an email to the course organizer with your information and motivation for joining the course. Do not use the online application. Thank you.


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