## 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:

1. Thermodynamics of Phase Transitions (liquid-gas phase transition, Maxwell construction)

2. Statistical Physics of Interacting Particles (cluster expansion of non-ideal gases)

3. Quantum Statistical Physics (interacting fermions and bosons, Bose-Einstein condensation)

4. Order-disorder Transitions (2D Ising model and mean-field interactions, Landau theory and critical exponents)

5. 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

### Transferable Skills

Reasoning about and modelling complex systems, numerical simulation, problem-solving, team work, communication.

## Timetable

Schedule

For detailed information go to Timetable in Brightspace

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

See Brightspace

Lectures, Exercise Classes and Homework.

## Assessment method

Written exam with homework bonus

## 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

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

## 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.