Mathematical Basis of Quantum Statistical Physics [MA5109]
Wintersemester 2013/14
Dr. David Reeb
Lecturer: | Dr. David Reeb | |
Lecture: | Mon 16:30-18:00, LMU, Theresienstr. 37, room A 450 | Anmeldung |
Exercises: | Thu 16:30-18:00 (bi-weekly), LMU, Schellingstr. 4, lecture hall H 030 dates: 24.10., 7.11., 21.11., 5.12., 19.12., 16.01., 30.01. |
Anmeldung |
News
- 31.01.2014: Everyone I know of who wants to take the oral examination on 12./24./26.02.2014 should have received an email today with the exact date and time. If not, please notify me as soon as possible.
- Oral examinations will be held on 12.02.2014, on 24.02.2014, and on 26.02.2014 (note the date change compared to the originally announced dates) at Garching Forschungszentrum, Boltzmannstr. 3, room 03.12.040. Please email me with your preferred date before the end of January (david.reebtum.de, or tell me after the lecture), and I will make up a schedule which I will then send to each of you individually. The relevant material is everything except for Chapter 0 (first lecture class). Feel free to email me with questions and we can also set up an office hour.
Contents
This course provides the abstract mathematical concepts necessary to treat quantum systems in equilibrium within the algebraic framework. The specific topics addressed are:C*-algebras, GNS construction, states, von Neumann algebras, quasi-local algebras and time-evolution (we did not get to the following topics: Tomita-Takesaki Modular Theory, KMS states and their properties and physical significance, relative entropy and other entropy measures).
- prereqs: basic notions of functional analysis; familiarity with quantum mechanics or statistical mechanics helpful but not necessary
- examination: oral (ca. 25min.)
Literature
- Bratteli/Robinson, "Operator Algebras and Quantum Statistical Physics", esp. certain sections from chapters 2 (vol. 1) and 5 (vol. 2)
- Takesaki, "Theory of Operator Algebras I", Springer. Chapter II on von Neumann algebras.
- Skoufranis, Notes on "Trace Class Operators" ^{}. Concise review of compact and trace class operators and their duality with B(H); in particular Theorem 23 is basic to the theory of von Neumann algebras ("normal states", "predual").
- Naaijkens, arXiv lecture notes ^{}. Sections 2.4 - 3.3 relating to chapter 3 of our lecture (last three lecture classes).
- Thirring, "Quantum Mathematical Physics", esp. chapter 2 of (former) volume 3 ("QM of atoms and molecules") and various parts of (former) volume 4 ("QM of large systems")
- Ohya/Petz: Quantum Entropy and Its Use (towards the end of the course; did not get to this material)
- my hand-written lecture notes: 14.10.2013, 21.10.2013, 28.10.2013, 04.11.2013, 11.11.2013, 18.11.2013, 25.11.2013, 28.11.2013, 02.12.2013, 09.12.2013, 16.12.2013, 09.01.2014, 13.01.2014, 20.01.2014, 27.01.2014
Exercises
- Exercise sheet 7 (30.01.2014) -- Solutions
- Exercise sheet 6 (16.01.2014) -- Solutions
- Exercise sheet 5 (19.12.2013) -- Solutions (see comments on Ex. 5.2)
- Exercise sheet 4 (05.12.2013) -- Solutions
- Exercise sheet 3 (21.11.2013) -- Solutions (26.11.2013: solution to Ex. 3.7(a) corrected)
- Exercise sheet 2 (07.11.2013) -- Solutions
- Exercise sheet 1 (24.10.2013) -- Solutions
- Initial test (14.10.2013) -- Solutions