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Quantum mechanics. Quantumfield theory --- Magnetic properties of solids --- Quantum Hall effect --- Hall quantique, Effet --- Quantum Hall effect.

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Topological concepts are essential to understand many of the most important recent discoveries in the basic physics of solids. Topology can be loosely defined as the branch of mathematics studying the properties of an object that are invariant under smooth distortions. Topological phases, as a result, show a kind of robustness and universality that is similar in spirit to the famous universality observed at continuous phase transitions, but with a very different microscopic origin. This chapter introduces some of the key examples of topological phases of matter and places them in the broader context of many-body physics. Einstein famously commented that statistical mechanics was one kind of physics whose basic principles would last forever, because they were based only on the assumption that our knowledge of a complex system is incomplete. Topological phases show how a kind of macroscopic simplicity and perfection can nevertheless emerge in many-particle systems, even in the presence of disorder and fluctuations that make a complete microscopic description impossible.

Condensed matter. --- Topology. --- Topological defects (Physics) --- Geometric quantum phases. --- Quantum Hall effect. --- Matière condensée --- Topologie --- Hall quantique, Effet --- Matière condensée --- Topological defects (Physics).

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Quantum Hall effect --- Quantum field theory --- Hall quantique, Effet --- Théorie quantique des champs --- 537.633 --- Electrical effects. Hall effect. Corbino effect. Gauss effect --- 537.633 Electrical effects. Hall effect. Corbino effect. Gauss effect --- Théorie quantique des champs

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A comprehensive collection of papers on theoretical aspects of electronic processes in simple and synthetic metals, superconductors, bulk and low-dimensional semiconductors under extreme conditions, such as high magnetic and electric fields, low and ultra-low temperatures. The main emphasis is on low-dimensional conductors and superconductors, where correlated electrons, interacting with magnetic or nonmagnetic impurities, phonons, photons, or nuclear spins, result in a variety of new physical phenomena, such as quantum oscillations in the superconducting state, Condon instability, Skyrmions and composite fermions in quantum Hall effect systems, and hyperfine field-induced mesoscopic and nanoscopic phenomena. Several new experimental achievements are reported that promise to delineate future trends in low temperature and high magnetic field physics, including the experimental observation of the interplay between superconductivity and nuclear spin ordering at ultra-low temperatures, new observations of Condon domains in normal metals, and an experimental proposal for the realisation of isotopically engineered, semiconductor-based spin-qubit elements for future quantum computation and communication technology.

Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Electricity & Magnetism --- Magnetic fields --- Superconductivity --- Quantum Hall effect --- Spintronics --- Champs magnétiques --- Supraconductivité --- Hall quantique, Effet --- Électronique de spin --- Congresses. --- Congrès --- Condensed matter. --- Optics. --- Electrodynamics. --- Solid state physics. --- Spectroscopy. --- Microscopy. --- Materials science. --- Optical materials. --- Electronic materials. --- Condensed Matter Physics. --- Classical Electrodynamics. --- Solid State Physics. --- Spectroscopy and Microscopy. --- Characterization and Evaluation of Materials. --- Optical and Electronic Materials. --- Electronic materials --- Optics --- Materials --- Material science --- Physical sciences --- Analysis, Microscopic --- Light microscopy --- Micrographic analysis --- Microscope and microscopy --- Microscopic analysis --- Optical microscopy --- Analysis, Spectrum --- Spectra --- Spectrochemical analysis --- Spectrochemistry --- Spectrometry --- Spectroscopy --- Chemistry, Analytic --- Interferometry --- Radiation --- Wave-motion, Theory of --- Absorption spectra --- Light --- Spectroscope --- Solids --- Dynamics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Qualitative --- Analytical chemistry