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Delta ITP

ITP Utrecht

  DELTA ITP

ADVANCED TOPICS IN THEORETICAL PHYSICS II (SPRING 2013)

FIELD THEORY IN CONDENSED MATTER




Summary
The course "Field Theory in Condensed Matter" is part of the Delta ITP, which is a joint initiative between the Universities of Leiden (UL), Utrecht (UU), and Amsterdam (UvA).

The lectures are given by professors from these three universities, on topics that change every year. The course is intended for PhD and Master students who have learned the basis of Quantum Field Theory.
It consists of three topics; for each one there are four lectures (2hrs each) and four exercise sessions (4hrs each). At the end of each modulus there is a written 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. The topics will be complemented by seminars given by experimentalists working in the subject, to give the students a better perspective of how the theoretical models connect to the real world.

The lectures are on Monday and this semester they will be in Utrecht.
Attention: The rooms reserved for the lectures and exercise sessions are in different locations in Utrecht University (De Uithof):
The lectures are on Monday at 11:00, in BBL 165 until 15/04 and in BBL 079 from 22/04 until the end of the semester.
The exercises are on Monday, from 13:15 - 17:00, in BBL 027 until 15/04 and in BBL 201 from 22/04 until the end of the semester.

Contents
1. Physics in two dimensions: the Quantum Hall effects
Prof. C. Morais Smith (UU)
The discovery of the Integer Quantum Hall Effect, nearly 35 years ago, has provided us with the first topological state of matter, i.e. systems which have an insulating bulk and a conducting edge. In addition, in a certain regime of parameters these edge currents are quantized and the Hall conductivity is an integer (in units of the quantum of conductance). This integer is connected to a topological invariant, the Chern number. Recently, it was proposed that in graphene, a 2D honeycomb lattice of Carbon atoms, it should be possible to realize another topological state of matter, namely the Quantum Spin Hall Effect. In this case, there are no quantized charge, but spin currents. In this course we will introduce the basic concepts to understand the fascinating behavior of topological states of matter.
Reading material: http://arxiv.org/abs/0909.1998.

2. Physics in one dimension: Luttinger liquids and bosonization
Prof. J. S. Caux (UvA)
Systems of interacting particles in reduced dimensionality offer a number of extremely interesting features which distinguish them from their higher-dimensional Fermi liquid-like brethren: examples include particle transmutation and quantum number fractionalization. In this course, the concept of the Luttinger liquid universality class will be presented, the formalism of bosonization will be exposed in technical detail, and illustrated by a number of examples from experimentally-realizable systems.

3. Random-matrix theory
Prof. C. Beenakker (UL)
The theory of random matrices originated half a century ago to describe the spectral statistics of atoms and nuclei. Applications to quantum dots (artifical atoms) followed, stimulated by developments in the field of quantum chaos, as well as applications to classical and quantum optics. Now a new state of matter with topological order (hosting exotic particles such as Majorana fermions) provides for a new arena of applications of random-matrix theory. We will give an overview of both the older and more recent developments.
Background reading: http://arxiv.org/abs/0904.1432.

Detailed program
Part I: from 11/02 - 11/03 - Quantum Hall effects
This part will be taught by Prof. C. Morais Smith (UU).
We will discuss:
The integer quantum Hall effect (11/02),
The fractional quantum Hall effect (18/02),
Quantum Hall Ferromagnets and Bilayer Quantum Hall systems (25/02),
The Quantum Hall Effect in graphene (04/03).
Exam about QHE on 11/03.

Part II: from 18/03 - 29/04 - 1D systems: bosonization
This part will be taught by Prof. J. S. Caux (UvA)
Easter vacation on 01/04
No lecture on 15/04 (exam week in Utrecht)
Final exam on 29/04.

Part III: from 06/05 - 17/06 - Random Matrix Theory
This part will be taught by Prof. Carlo Beenakker (UL).
No lecture on 20/05 (Pentecost)
No lecture on 03/06
Exam on 17/06.

Contact:
Prof. Cristiane Morais Smith
Institute for Theoretical Physics
Utrecht University
Minnaert building, room 306
tel: +31 30 253 30 62
e-mail: c.demoraissmith@uu.nl



Last update: 01-02-2019, 14.12