We first will combine notions discussed in Statistical Physics 1 and Quantum Mechanics to derive a conceptual picture of Bose-Einstein condensation. Subsequently, we will increase the complexity of the systems to allow for interactions between objects. This requires the introduction of approximation methods. We will specifically discuss the virial expansion, the van der Waals equation of state, low- and high-temperature expansions, and mean field theory. This will give us handles to study complex problems like the gas-liquid phase transition, the spontaneous magnetization of a system of interacting spins, and the interaction between charged objects immersed in a salt solution. Further we will extend our studies towards systems that are out of equilibrium. The notion of steady-state will be introduced. Approximation methods will be developed that permit to describe how systems reach to equilibrium. We will see how system noise is deeply connected to the way the system approaches towards equilibrium.
After sucessul completion of the course students have knowledge about Bose-Einstein condensation, mean-field theory, virial expansion, Landau theory, linear response, the fluctuation-dissipation theorem, and the Fokker-Planck equation. Students will be able to apply those concepts to examples from solid-state physics to biology and finance.
Mode of instruction
Lectures and Exercise Classes
Lecture notes, additional readings and assignments will be provided.
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Daijiro Yoshioka, Statistical Physics, An Introduction
Excerpts from (will be provided): Claude Garrod, Statistical Mechanics and Thermodynamics; Frederick Reif, Fundamentals of Statistical and Thermal Physics