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402-0861-00L 10 Credits DR , MSC D-ITET , D-MATH , D-PHYS
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Statistical Physics

Lecturers & Examiners: Prof. Dr. Gian Michele Graf
VVZ CR n/a

Last Updated: 2026-02-05 16:14:58

Abstract

The lecture covers the concepts of classical and quantum statistical physics. The discussion ranges from foundations to specific systems, including their formalisms and techniques, such as bosonic and fermionic gases, and magnetism. Phenomena, most notably phase transitions, are treated by methods such as exact solutions, mean-field approximations, and the renormalization group.

Objective

This lecture gives an introduction to the basic concepts and applications of statistical physics for general use in physics and, in particular, as preparation for theoretical solid-state physics.

Content

Thermodynamics: Laws of thermodynamics, thermodynamic potentials, phenomenology of phase transitions of first and second order. Van der Waals gas-liquid transition. Classical statistical physics: micro-canonical-, canonical-, and grand canonical ensembles; the arrow of time, applications to interacting systems, and cumulant expansion. Quantum statistical physics: density matrix, ensembles, ideal quantum gases, fermions and bosons, second quantization, statistical interaction. Degenerate fermions: Fermi gas, electrons in magnetic field. Bosons: photons and phonons, Bose-Einstein condensation. Bogolyubov’s theory of superfluidity and liquid Helium. Magnetism: Ising-, XY-, Heisenberg models, exact solutions, mean-field theory, Peierls' argument on long-range order, Berezinskii-Kosterlitz-Thouless transition. Landau theory of phase transitions and symmetry. Critical phenomena: scaling theory, universality, and the renormalization group.

Resources

Lecture Notes

Lecture notes available in English.

Literature

No specific book is used for the course. Relevant literature will be given in the course.

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 35 minutes
Die effektive Prüfungsdauer ist 30min.Aus technischen Gründen wird 35min angezeigt.The effective duration of the exam is 30 minutes.For technical reasons it shows 35min.

Course Components

Type Title Time & Place Hours
lecture Statistical Physics
  • Tue 13:45-15:30 (HPV G 5)
  • Wed 13:45-15:30 (HPV G 5)
4 h weekly
exercise Statistical Physics
  • Tue 15:45-17:30 (HCI J 4)
  • Wed 11:45-13:30 (HIT H 42)
  • Wed 11:45-13:30 (HIT J 51)
2 h weekly

Offered In

  • Mathematics Master
    • Application Area (Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area. Credits from other application areas cannot be recognised for further application areas.)
      • Theoretical Physics (In the Master's programme in Applied Mathematics 402-0205-00L Quantum Mechanics I is eligible as a course unit in the application area Theoretical Physics, but only if 402-0224-00L Theoretical Physics wasn't or isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
    • Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  • Physics Master
    • Core Courses (One Core Course in Experimental or Theoretical Physics from Physics Bachelor is eligible; however, this Core Course from Physics Bachelor cannot be used to compensate for the mandatory Core Course in Experimental or Theoretical Physics. For the category assignment keep the choice "no category" and take contact with the Study Administration ( ) after having received the credits.)
  • Doctorate Mathematics (More Information at: )
    • Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
  • Quantum Engineering Master
    • Core Courses (A minimum of 24 credits must be obtained from core courses during the MSc QE, course selection is subject to the tutor's agreement.)
      • Physics Core Courses (These core courses target students with an engineering background and all those who need additional physics foundations.)