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Statistical Physics b


Admission Requirements

Bachelor in Physics and knowledge of basic statistical mechanics.


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.


  • 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).

Generic skills (soft 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.


Physics Schedule

Mode of instruction

Lectures and tutorials.

Assessment method

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


To have access to Blackboard you need a ULCN-account.Blackboard UL

Reading list

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


Lecturer: Dr. Luca Giomi