Statisitical Physics 1, Quantum Mechanics 2
The goal of Statistical Physics 2 is to understand the physics behind phase transitions in systems of interacting particles using the statisitical 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. One of the exercise classes will be an open numerical experiment using Python.
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)
- Fluctuations (Brownian motion, fluctuation-dissipation, Fokker Planck equation, Black-Scholes in finance)
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. Throughout the course a strong link is made between theoretical concepts, experimental observation and modern research. Examples will be spread across the various disciplines relevant to the research groups in the institute.
At the end of the course you will be able to:
apply the methods of statisitcal physics to simple examples in solid-state physics, biology and finance.
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 phenemenon of Bose-Einstein condensation
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 systems where fluctuations become important on a macroscopic scale
Problem-solving, team work, communication
Mode of instruction
Lectures, Exercise Classes and Homework. A solution will be provided to follow these activities online.
Written exam with homework bonus
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)