Department Mathematik



(Tentative) website for the lecture

Mathematical statistical physics

SoSe 2017 Prof. Dr. Sven Bachmann and Prof. Dr. Belen Paredes

Exercise Sessions (start in the second week): Wednesday 14-16 (B004)

Tutorials (start in the second week): Thursday 14-16 (B005)

Preliminary content of the (mathematical part) of the lectures:

  1. Ideal gases and Bose-Einstein condensation
  2. Thermal equilibrium: general theory
  3. Phase transitions in quantum spin systems

Exam: The final exam will take place on Thursday, July 27 in room B004, starting at 12.30. It will be made of two parts corresponding to the two parts of the lecture. For the exam to be passed, students must pass both parts independently. For the mathematics part, a bonus of +5% will be added to the exams total points, if the student has obtained at least 50% of the maths exercise points during the semester.

Lecture notes:

Part 1

Part 2

Part 3

Supplementary material (for those who are interested):

C*-algebras, states and representations

KMS states

Free dynamics on Fock space

Phase transitions in quantum spin systems

Exercise sheets:

Problem Sheet 1 (Solution)

Problem Sheet 2 (Solution)

Problem Sheet 3 (Solution)

Problem Sheet 4 (Solution)

Problem Sheet 5 (Solution and Solution to Ex. 4)

Problem Sheet 6 (Solution)


  1. 04.05.2017: Inequivalent representations
  2. 10.05.2017: Trace class and Hilber-Schmidt ideals (Literature: Reed-Simon, Vol. 1, Chaper VI.6)
  3. 18.05.2017: Weyl asymptotics
  4. 22.06.2017: Duhamel principle and Golden-Thompson inequality