This is an advanced master level  course, also suitable for PhD students and postdocs. This Spring semester course will be divided into three 5-weeks modules. For each module there are four lectures (3 hrs) and four exercise sessions (3 hrs). At the end of each modules there is an exam. 

PhD students are not obliged to do the exams, which are meant for Master students who intend to use this course as part of their Master Program. 
Please note that to get the full 6EC credit, students must take the exam for each of the three modules. The final grade is the average of the three exams.

Summary

Lectures will take place on Mondays at 11:15 - 13:00, followed by a study/exercise session from 13:45 - end. The location of this semester's course will be Utrecht University.   

Module 1: Bosonization - Dirk Schuricht (UU) 

Lectures: Feb 8, 15, 22, 29

EXAM March 7

In this module, we discuss the basics of the bosonisation technique, which provides a universal description of the low-energy properties of generic one-dimensional systems. We apply this technique to several examples, including quantum wires and spin chains.

Course material: 

D. Sénéchal, An introduction to bosonization, arXiv:cond-mat/9908262
T.

Giamarchi, Physics in one dimension, OUP 2004

Module 2: Introduction to the Lieb-Liniger model - Jean-Sébastien Caux (UvA)  

Lectures: Mar 14, 21, Apr 11


EXAM: Apr 18 

1. Interacting bosons in one dimension. The Lieb-Liniger model. Coordinate Bethe Ansatz.


2. Building the eigenstates basis. Bethe equations and their solutions. Properties of Bethe wavefunctions.


3. Going towards the thermodynamic limit. The ground state of the repulsive gas and the Lieb equation. Zero temperature physical properties.


4. Excitations. Lieb Type 1 and 2 modes. Link with bosonization. Calculation of effective Luttinger theory parameters.


5. Finite temperature equilibrium. The Yang-Yang formalism.


6. Advanced topics. The attractive gas. Algebraic Bethe Ansatz. Matrix elements. Correlation functions. Out-of-equilibrium effects and Quantum quenches. The Quench Action formalism.

Module 3: Polymer physics: Physics at critical points - Helmut Schiessel (UL) 

Lectures: Apr 25, May 2, 9, 23


EXAM: May 30

In this module we discuss the physics of polymers. The exciting point is that a polymer (by the very fact that it is extremely long) is extremely close to a critical point. Thus chemistry does not matter much. The universal behavior of polymers leads to an elegant geometrical description in terms of “blobs” that was pioneered by the late Pierre-Gilles de Gennes who was called by the Nobel Committee 'the Isaac Newton of our time'.

Course Material:

Lecture notes will be provided, partially based on Pierre-Gilles de Gennes’ Scaling Concepts in Polymer Physics.

Contact: 

Dr. Koenraad Schalm  Institute-Lorentz for Theoretical Physics | Leiden University

Prof. Cristiane Morais Smith  Institute for Theoretical Physics  | Utrecht University 

Prof. Jean-Sébastien Caux  Institute for Theoretical Physics | Institute of Physics | University of Amsterdam