## Admission Requirements

Statisitical Physics 1, 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. Fluctuations and stochasticity (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. 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.

## 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

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

Problem-solving, complex system modelling, numerical simulation, team work, communication

## Timetable

Schedule

For detailed information go to Timetable in Brightspace

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## 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

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.

## Contact

Dr. M.J.A. de Dood (Michiel) Dr. M. Serra Garcia

## Remarks

none