# Statistical Physics b

Vak
2024-2025

Bachelor in Physics, Statistical Physics a and knowledge of basic statistical mechanics.

## Description

What do a magnet, a Bose-Einstein condensate and a flock of birds have in common? All these systems exhibit a collective behavior and have large-scale physical properties that cannot be understood in terms of a simple extrapolation of the properties of a few particles. Conversely, systems comprising many interacting subunits often present entirely new properties, that scientists refer to as emergent.

Statistical Physics B, is the second part of a two-part introductory course on emergent phenomena in equilibrium and non-equilibrium systems. The course provides an introduction to phase transition and collective behavior in non-equilibrium systems, with special attention for active (i.e. self-driven) particles. The first (compulsory) part of this course is given in Statistical Physics A and is focused on phase transitions and critical phenomena at equilibrium.

The course consists of 4 lectures and 1 tutorial. During the tutorial, the students will work in groups and use interactive software (developed by former MSc student Leandros Talman) to simulate the dynamics of bird flocks.

Topics

• Introduction to collective behavior: flocking, schooling, swarming etc.

• The XY-model and the Mermin-Wagner theorem.

• The Vicsek model.

• Giant density fluctuations.

## Course Objectives

The aim of the course is to develop a strong foundation in advanced statistical mechanics with an emphasis on emergent phenomena. Furthermore, the course aims to provide the students with a toolbox of mathematical techniques that can be readily used in theoretical and experimental research projects.

Specifically, at the end of the course, successful students will have learned how to:

• Model the relaxation dynamics of equilibrating fields.

• Construct a simple phenomenological hydrodynamic theory of self-propelled objects.

• Calculate number density and order parameter fluctuations from hydrodynamic equations instead of the Hamiltonian.

• Perform simple numerical simulations and analyze data (but no coding will necessary).

## Timetable

Physics 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.

See Brightspace

## Assessment method

Take-home exam consisting of a an analytical and a computational exercise.

Reading material (research papers and notes) will be provided during the lectures.

## Registration

As a student, you are responsible for registering for each course component. This can be done via Mystudymap. You do this twice a year: once for the courses you want to take in semester 1 and once for the courses you want to take in semester 2.

Registration for courses in the first semester is possible from July onwards; registration for courses in the second semester is possible from December onwards. For more information, see this page

Please note that it is mandatory for all students to register for their exams. This can be done up to and including 10 calendar days prior to the exam or up to five calendar days in case of a retake exam (retake registration opens 30 days before the retake takes place). You cannot participate in the exam or retake without a valid registration in My Studymap

## Contact

Lecturer: Dr. Luca Giomi

## Remarks

Transferable skills

At the end of the course, students will have been trained how to:

• Work in teams.

• Write a scientific essay based on original results.