The book contains the worked out lecture notes of the courses delivered at the summer school in Les Houches. They address graduate students and are of interest for researchers as well. The book can be used as an introduction into three closely related fields: anyons and fractional statistics, fractional quantum Hall effect and knot theory. The theoretical papers are occasionally completed by reports on experimental techniques, and besides of physics some application to biological systems can be found.
From the contents: Electrons in a Flatland.- The Quantum Hall Effect: Novel Excitations and Broken Symmetries.- Aspects of Chern-Simons Theory.- Anyons.- Generalized Statistics in One Dimension.- Lectures on Non Perturbative Field Theory and Quantum Impurity Problems.- Quantum Partition Noise and the Detection of Fractionally Charged Laughlin Quasiparticles.- Mott Insulators, Spin Liquids and Quantum Disordered Superconductivity.- Statistics of Knots and Entangled Random Walks.- Twisting a Single DNA Molecule: Experiments and Models.- Introduction to Topological Quantum Numbers.- Geometrical Description of Vortices in Ginzburg-Landau Billiards.- The Integer Quantum Hall Effect and Anderson Localisation.- Random Magnetic Impurities and Quantum Hall Effect.
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