## Admission Requirements

Statisitical Physics 1, Quantum Mechanics 2

## Description

The goal of Statistical Physics 2 is to find a macroscopic description of systems where interactions between particles play an important role. In this course you will combine notions discussed in Statistical Physics 1 and Quantum Mechanics 2 to derive a conceptual picture of Bose-Einstein condensation and the different phases of liquid Helium. Subsequently, we will increase the complexity of the systems to allow for interactions between particles, which 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. You will explore systems where fluctuations become important and shed some light on the often-used fluctuation-dissipation theorem.

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 and include solid state physics as well as biological systems.

## Course objectives

At the end of the course you will be able to:

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.

Describe quantum statisitical physics using the quantum canonical ensemble

Calculate the quantum mechanical partitition function and entropy

Apply quantum statistical physics to an ideal quantum gas

Explain Bose-Einstein condensation

Compute phase transitions in a two-dimensional Ising model

Formulate the mean-field approximation for the Ising model

Describe the thermodynamics of phase-transitions

Give examples of systems where fluctuations become important on a macroscopic scale

Formulate and apply the fluctuation-dissipation theorem in several practical situations

Apply the above concepts to examples form solid-state physics and biology.

## Timetable

## Mode of instruction

Lectures and Exercise Classes

## Assessment method

Written exam and homework bonus

## Blackboard

Lecture notes, additional readings and assignments will be provided. To have access to Blackboard you need a ULCN-account.Blackboard UL)

## Reading list

Robert H. Swendsen, An introduction to Statistical Mechanics and Thermodynamics, Oxford University Press, Oxford, UK (2012), ISBN 978-0-19-964694-4

Additional literature: Linda E. Reichl, A Modern Course in Statistical Physics, 4th edition, Wiley-VCH Verlag GmbH, Weinheim, Germany (2016), ISBN 978-3-527-41349-2