Admission requirements
Prior knowledge of Statistical Physics 1 and Quantum Mechanics 2.
Description
The goal of Statistical Physics 2 is to understand the physics behind phase transitions in systems of interacting particles using the statistical description of ensembles.
The course is structured in five connected themes of increasing complexity that discuss the physics of the different states of matter and the phase transition. Each theme consists of 2 lectures and exercise classes. Python exercises and numerical skills are an integral part of the course. One of the exercise classes will be devoted to a collaborative numerical exploration of the 2D-Ising model.
Themes in Statistical Physics 2:
- Thermodynamics of Phase Transitions (liquid-gas phase transition, Maxwell construction)
- Statistical Physics of Interacting Particles (cluster expansion of non-ideal gases)
- Quantum Statistical Physics (interacting fermions and bosons, Bose-Einstein condensation)
- Order-disorder Transitions (2D Ising model and mean-field interactions, Landau theory and critical exponents)
- Far-from-equilibrium systems (Brownian motion, fluctuation-dissipation, Fokker Planck equation, Non-equilibrium free energy and fluctuation theorems)
The treatment of the topics inside these themes will build on prior knowledge from Statistical Physics 1 and Quantum Mechanics 2 with the goal to describe more realistic systems. This can only be achieved through the use of approximation methods or numerical experiments. Throughout the course a strong link is made between theoretical concepts, experimental observation and modern research directions. Examples will be spread across the various disciplines relevant to the research groups in the institute.
Course objectives
At the end of the course you will be able to:
Apply the methods of statistical physics to simple examples in solid-state physics, biology.
Describe interacting systems in the microcanonical, canonical and grand-canonical ensemble
Give expressions for the equation of state of non-ideal gases in terms of cluster integrals (virial expansion)
Explain the phenomenon of Bose-Einstein condensation
Recognize and leverage universality in physics (very different systems exhibiting equivalent behaviors)
Use the Metropolis algorithm to analyze phase transitions in the two-dimensional Ising model
Construct a mean-field approximation for systems of interacting particles
Explain the use of an order parameter and its role in phase transitions
Analyze interacting systems close to a phase transition using Landau theory, critical temperature and critical exponents
Describe out-of-equilibrium systems and systems where fluctuations become important on a macroscopic scale
Schedule
The timetables are available through My Timetable (see the button in the upper right corner).
Teaching method
See Brightspace
Lectures; Exercise Classes and Homework.
Assesment method
Written exam with homework bonus
Resit, review & feedback
Examinations are held twice during the academic year for each component offered in that academic year. Midterm tests cannot be retaken. The Board of Examiners determines the manner of resit for practical assignments.
For review and feedback, see Brightspace.
Reading list
Linda E. Reichl, A Modern Course in Statistical Physics, 4th edition, Wiley-VCH Verlag GmbH, Weinheim, Germany (2016), ISBN 978-3-527-41349-2
Robert H. Swendsen, An introduction to Statistical Mechanics and Thermodynamics, Oxford University Press, Oxford, UK (2012), ISBN 978-0-19-964694-4 (used in the Statistical Physics 1 course)
Registration
Enrolment through MyStudyMap (button in upper right corner) is mandatory. General information about course and exam enrolment is available on the website.
Contact
For substantive questions, contact the lecturer(s) (listed in the right information bar).
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.