Statistical Physics and Condensed Matter Theory 1 (September-October 2017)
Time and location of the lectures:
Tuesdays 11:00-15:00, Science Park C0.110 and Fridays 13:00-17:00, Science Park C0.05
Final exam:
Monday 23 October 2017, 9:00-12:00, SP Tentamenzaal USC, Sporthal 2
Retake exam:
rescheduled to Monday 8 January 2018, 16:00-19:00, SP D1.113
You can also have a look at previous editions in 2016, 2015 and 2014.
Assistants
Extra question sessions
Moos and Sergio have reserved Thursdays 11:00-12:00 for extra catch-up sessions. These will take place in room SP A1.11 (except on 14 Sept. in D1.162).
Course objectives
This course will provide a thorough grounding in fundamental aspects of modern theoretical statistical and condensed matter physics. The lectures will cover all necessary formalism, but also emphasize the applicability and usefulness of the methods in the context of contemporary experimental and theoretical research issues.
Contents
Starting from basic notions of statistical mechanics and quantum theory, the students will be progressively introduced to the formalisms of operatorial quantization, path integrals and functional field integration. The wide applicability of these methods in condensed matter and statistical physics will be emphasized by addressing topics such as (among others) low-dimensional interacting fermionic and spin systems, spin-charge separation and the Luttinger liquid, the Kondo effect, broken symmetry and Bose-Einstein condensation, superfluidity and superconductivity.
Materials
Class notes are available
here. These are broadly based on the book
Condensed Matter Field Theory by B. D. Simons and A. Altland. This book has been selected due to its rather successful attempt to "provide a bridge between formal manipulations and research-oriented thinking", which fits perfectly well in a modern masters-level program aimed at forming a new generation of researchers and thinkers.
Recommended additional reading
Plan of the course
Session 1 (Tue 5/9/2017, JvW):
Introduction. Harmonic chain: classical [1.1] and quantum [1.4] cases. [eboard notes 1a, 1b]
Session 2 (Fri 8/9/2017, JSC):
Operatorial quantization [2.1].
Session 3 (Tue 12/9/2017, JvW):
Applications of operatorial quantization [2.2]. [eboard notes]
Session 4 (Fri 15/9/2017, JvW):
Applications of operatorial quantization [2.2]. [eboard notes]
Session 5 (Tue 19/9/2017, JvW):
Brownian motion and classical path integrals.
Feynman path integral in quantum mechanics [3.1], [3.2]. [eboard notes]
Session 6 (Fri 22/9/2017, JSC):
Functional field integral. Many-body path integral [4.1]. [eboard notes]
Session 7 (Tue 26/9/2017, JSC):
Field integral for the quantum partition function [4.2]. [eboard notes]
Session 8 (Fri 29/10/2017, JSC):
Perturbation theory. General structures[5.1]. Low-order expansions [5.1]. [eboard notes]
Session 9 (Tue 3/10/2017, JvW):
Ground-state energy of the interacting electron gas [5.2]. [eboard notes]
Session 10 (Fri 6/10/2017, JvW):
Broken symmetry and collective phenomena. Mean-Field theory [6.1]. Plasma theory of the interacting electron gas [6.2]. [eboard notes]
Session 11 (Tue 10/10/2017, JSC):
Superconductivity [6.4]. [eboard notes]
Session 12 (Fri 13/10/2017, JSC):
Linear response theory [7.2]. Correlation functions [7.3]. [eboard notes]
Session 13 (Tue 17/10/2017, JSC):
Imaginary time correlation functions. Example problem (from Final 2016): photoemission spectroscopy [eboard notes]
Buffer
Session 14 (Fri 20/10/2017, JvW):
General revision
Please view this as an indication only: since my coverage of the material will differ somewhat from the book, please check and rely on your class notes to revise the more specific contents we discussed.
Suggested exercises
Collective Phenomena
The Operator Formalism
Path Integrals
Functional Integrals
Perturbation Theory
Effective Theories
Response Functions
Past exams