Quantum Hall systems
Braid groups, composite fermions and fractional charge
International Series of Monographs on Physics Series, Vol. 119

This book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It covers the fundamental problems of two-dimensional quantum statistics in terms of topology and the corresponding braid group formalism for composite fermions, and the main formalism used in many-body quantum Hall theories, the Chern-Simons theory. Numerical studies are introduced for spherical systems and the composite fermion theory is tested. The book introduces the concept of the heirarchy of condensed states, the BCS paired Hall state, and multi-component quantum Hall systems and spin quantum Hall systems.

Introduction. Topological methods for description of quantum many-body systems. Quantization of many-particle systems and quantum statistics in lower dimensions. Topological approach to composite particles in two dimensions. Many-body methods for Chern-Simons systems. Anion superconductivity. The fractional quantum Hall effect in composite fermion systems. Quantum Hall systems on a sphere. Pseudopotential approach to the fractional quantum Hall states.

Lucjan Jacak is a professor at the Institute of Physics, Wroclaw University of Technology. He was Director of the Institute of Physics in 1991-1996 and Pro-Rector of Wroclaw University of Technology during 1996-1999. He has received various awards for his work. Piotr Sitko is an associate professor at the Institute of Physics, Wroclaw University of Technology. He received two awards in 1995 and 1998. Konrad Wieczorek is an associate professor at the Institute of Physics, Wroclaw University of Technology. Arkadiusz Wójs is an assistant professor at the Institute of Physics, Wroclaw University of Technology. He received three awards during 1996-1998.