One-Dimensional Physics: From Quantum Wires to Quantum Field Theory
Lecture in "Vertiefungsgebiet Theoretische Physik" (Module Phy-Ma-Vert)
The lecture is suited for Master and advanced Bachelor students, as well as PhD students. A good understanding of elementary quantum mechanics as well as basic knowledge of solid state physics is strongly recommend. The lecture will be given in English.
Content: This lecture will explain how one-dimensional systems can be analysed theoretically, and how dramatically different they are from two- and three-dimensional systems. We will cover exciting physical phenomena such as spin-charge separation, understand in what sense bosons, fermions, and spins are the same in one dimension, and provide an introduction to the field theoretical description of one-dimensional systems, as well as the renormalisation group approach. More detailed planning:
1) Examples for one-dimensional physics
2) Phenomeonological bosonization
3) Quantum anomalies and normal ordering
4) Luttinger liquids, and formal bosonization
5) Spin charge seperation
6) Renormalization group and sine-Gordon terms
7) Jordan-Wigner transformation of spin chains
8) Applications of bosonization and Luttinger liquid physics: impurities in quantum wires, conductance quantization, quantum Hall physics in coupled wires
Dates: Monday, 6th DS, BZW/A120 and Wednesday, 5th DS, SE2/122/U
First lecture: Monday, April 03, 2017, 6th DS, BZW/A120
Formate: 3 SWS lecture / 1 SWS excercise class (students who follow this course in the framework of the module Phy-Ma-Vert have to achieve 50% of the points in the problem sets on average).
Problem sets:
1) Problem set 1
2) Problem set 2
3) Problem set 3
4) Problem set 4
5) Problem set 5
Literature:
1) T. Giamarchi, Quantum Physics in One Dimension
2) A. O. Gogolin, A. A. Nersesyan, A. M. Tsvelik, Bosonization and Strongly Correlated Systems
3) J. von Delft, H. Schoeller, Bosonization for Beginners - Refermionization for Experts, arXiv:cond-mat/9805275
4) D. Sénéchal, An introduction to bosonization, arXiv:cond-mat/9908262
5) J. W. Negele, H. Orland, Quantum Many-Particle Systems
Contact: should you have any questions relating to the lecture, please contact Tobias Meng.