Fachbereich Mathematik

Seminar on Foundations of Statistical Mechanics

Winter semester 2022

  • Description: While statistical mechanics is widely used in physics, experts are still debating its foundations, about issues such as, what is the justification for the use of ensembles? Which of the varying definitions of entropy and thermal equilibrium are the most fundamental? This seminar will focus on foundational questions of statistical mechanics. We will mainly focus on quantum statistical mechanics (as opposed to classical statistical mechanics). This seminar fits well after the lecture "Mathematical Statistical Physics" in the past summer semester but does not require it.
  • Key themes: concepts of entropy and thermal equilibrium, random matrices, eigenstate thermalization hypothesis, typicality theorems.
  • Prerequisites: Analysis 1 and 2, linear algebra, quantum mechanics (QM). Recommended: courses in probability theory and/or statistical physics.
  • Studiengänge: B.Sc., B.Ed., M.Sc., M.Ed. in math or physics or mathematical physics.
  • ECTS: 3 credits.
  • Language of presentation: English
  • On campus or online? On campus only, unless the covid situation changes dramatically for the worse.
  • Talks: 90 minutes, one talk per week
  • List of talks:
    Date Speaker Title
    25.10.2022 C. Rubiliani Random matrices and their use in statistical mechanics
    01.11.2022 public holiday university closed
    08.11.2022 J. Garrels Approach to macroscopic thermal equilibrium
    15.11.2022 M. Wesle The thermodynamic limit in quantum mechanics
    22.11.2022 B. Poudyal Normal typicality
    29.11.2022 C. Igelspacher Definitions of entropy
    06.12.2022 S. Höfer Canonical typicality
    13.12.2022 no talk
    20.12.2022 S. Roy Approach to microscopic thermal equilibrium
    10.01.2023 no talk
    17.01.2023 T. Grickscheit The GAP measure
    24.01.2023 A. Jozani Smoothness of GAP-typical wave functions
  • Literature: will be recommended individually by topic of the presentation.