## Admission Requirements

Bachelor in Physics 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).

## 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.

## Timetable

## Mode of instruction

Lectures and tutorials.

## Assessment method

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

## Blackboard

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.

## Contact

Lecturer: Dr. Luca Giomi