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Course Code : | 2001WETSSP |

Study domain: | Physics |

Academic year: | 2020-2021 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | Exam contract not possible |

Language of instruction: | English |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Jacques Tempere |

At the start of this course the student should have acquired the following competences:

general notion of the basic concepts of

specific prerequisites for this course

- general knowledge of the use of a PC and the Internet

general notion of the basic concepts of

You will need to make graphs of your results on a computer, and you need to be able to do simple calculations on the computer (find roots of equations, numerical integration).

specific prerequisites for this course

You need to have followed a basic course on solid state physics, and be familiar with: the fermi sphere, phonons, the Drude and Sommerfeld models for a metal, crystal lattices and band structure. Also a basic knowledge of quantum mechanics is required, in particular second quantization.

- You have learned how to set up the second quantized Hamiltonian for a solid, and how to treat the electron-electron and electron-phonon interactions up to lowest order. You can apply this technique to calculate the energy dispersion and the lifetime of the polaron.
- You can write down Feynman diagrams for condensed matter problems, and calculate Green's functions and the amplitudes corresponding to those Feynman diagrams.
- You know how to interpret Green's functions, in particular how to extract quasiparticle energies and lifetimes from them.
- You can apply the diagrammatic technique to calculate dielectric functions, optical response, plasmon and polariton dispersion relations, and the conductivity of materials.
- You are familiar with Kubo response theory, and can calculate correlation functions and response of a material to an external perturbation.
- You are familiar with the Bardeen-Cooper-Schrieffer theory of superconductivity, and you can apply this theory to calculate basic properties of superconductors, such as the critical temperature, the critical magnetic field, the specific heat and the isotope effect.

First, we review the second quantization formalism, and apply it to set up the many-body problem for a solid in a general form, including electron-electron interactions and interactions between electrons and various lattice excitations. Then, we apply both perturbational methods and variational methods to calculate material properties, such as effective masses of electrons, bulk moduli, etc.

To overcome the limitations of perturbation theory, we need to systematize the way in which perturbation series are set up. For this purpose, we introduce Green's functions, and see how to interpret them, in particular how to extract material properties from Green's functions. To calculate the Green's function, we introduce the Gell-Man & Low theorem, Wick's theorem, vacuum polarization. We find that Feynman diagrams allow to calculate the Green's function in a systematic manner, and that they can be resummed using Dyson series. Diagrammatics allows to calculate the amplitudes corresponding to particular Feynman diagrams.

Then, we apply the diagrammatic techniques to calculate dielectric functions, the optical response, plasmon and polariton dispersion relations, and the conductivity of materials. This illustrates the use of the Green's functions and Feynman diagrams in a concrete many-body problem.

The optical response brings us to consider in the next part of the course Kubo response theory, for more general cases such as magnetic response.

Finally, we venture into a regime where perturbation theory around the Fermi sphere fails, and a variational approach shows the way forward: the Bardeen-Cooper-Schrieffer theory for superconductivity. We review the basic properties and experiments that led to the development of that theory, set up the theory, and calculate basis properties such as the critical temperature and critical magnetic field from it.

The course has an international dimension.

Class contact teachingLectures Practice sessions

Personal workAssignments Individually

**5.3 Facilities for working students ***

Others

Personal work

Others

Separate contact moments are possible after making an appointment. The exercises done in self-study can be discussed after appointment.

Continuous assessmentParticipation in classroom activities

Written assignmentWith oral presentation

Written assignment

Your course notes taken during the contact moments.

Printed course notes in English will be made available through the university reprography and will be placed on blackboard.

Most material covered in the course can also be found in:

"Solid State Physics, essential concepts", David W. Snoke, Pearson publishing, 2009

"Condensed Matter Field Theory", Altland and Simons, Cambridge University Press, 2006

"Quantum theory of many-body systems", Fetter and Walecka, McGraw Hill

Prof.dr. Jacques Tempere

Dept. Physics, CDE, room N0.17

03/265 2688