Statistical Physics and Condensed Matter Theory I

Course manual 2018/2019

Course content

Starting from basic notions of statistical mechanics and quantum theory, the students will be progressively introduced to the formalisms and models of modern condensed matter theory. The basic physical principles underlying emergent phenomena will be discussed in reference to (among others) interacting bosonic, fermionic, and spin systems; broken symmetry in magnetism, Bose-Einstein condensation, and superconductivity; and Fermi liquid theory. The universal applicability of the methods used in these discussions, like Ginzburg-Landau theory, second quantisation, path integrals, and functional field integration, will be emphasized.

Study materials

Literature

• Optional: T. Lancaster and S. J. Blundell, 'Quantum Field Theory for the Gifted Amateur', Oxford University Press.

• Optional: A. Altland and B. Simons, 'Condensed Matter Field Theory', Cambridge University Press.

Other

• Lecture notes (see Canvas page for this course).

Objectives

1. The student will be able to recognise, explain, and work with basic notions of condensed matter physics, including symmetries, order parameters, fluctuations, Ginzburg-Landau theory, the Goldstone theorem, Noether's theorem, the Mermin-Wagner theorem, and many-body states.
2. The student will be able to recognise and look for prototypical types of order, inlcuding charge order, spin waves, magnetism, Bose Einstein condensation, metals and superconductivity.
3. The student will be able to explain and to do calculations involving second quantisation, Hostein-Primakoff transformations, Bogoliubov transformations, propagators, correlation functions, Hamiltonian and Lagrangian formulations, Grassmann variables, partition functions, Wick’s theorem, and Euler-Lagrange equations.
4. The student will be able to do calculations within the path integral formalism, involving for example Feymnan path integrals, coherent states, functional integrals or diagrams.
5. The student will be able to recognise and to apply the basic approximation techniques of condensed matter physics, including mean field theory, Hubbard-Stratonovic transformations, many-body perturbative expansions (Schrieffer-Wolff or diagrammatic), and resummations (RPA).

Teaching methods

• Lecture
• Self-study
• Supervision/feedback meeting

The lectures will cover the main aspects of condensed matter theory. Students are expected to study the more detailed material presented in the lecture notes by themselves, and practice by themselves using the examples and exercised provided throughout the notes. A supervised forum for discussing the text and exercises of the notes will be provided. The students are also expected to prepare more advanced exercise sets for weekly tutorial meetings, during which the most important aspects in each set will be highlighted and discussed collaboratively in a supervised setting.

Learning activities

Attendance

Requirements concerning attendance (OER-B).

Additional requirements for this course:

none

Assessment

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. J. van Wezel

Teaching Assistants

• Schelto Crone
• Boris Ponsioen
• Yuan Miao