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For emerging energy saving technologies superconducting materials with superior performance are needed. Such materials can be developed by manipulating the "elementary building blocks" through nanostructuring. For superconductivity the "elementary blocks" are Cooper pair and fluxon (vortex). This book presents new ways how to modify superconductivity and vortex matter through nanostructuring and the use of nanoscale magnetic templates. The basic nano-effects, vortex and vortex-antivortex patterns, vortex dynamics, Josephson phenomena, critical currents, and interplay between superconductivity and ferromagnetism at the nanoscale are discussed. Potential applications of nanostructured superconductors are also presented in the book.

Quantum mechanics. Quantumfield theory --- Thermal properties of solids --- Electrical engineering

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The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.

Mathematics --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- Thermal properties of solids --- supergeleiding --- thermodynamica --- quantummechanica --- hoge temperatuur supergeleider --- supergeleiders --- wiskunde --- fysica

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During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg-Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg-Landau parameter kappa. Key topics and features of the work: * Provides a concrete introduction to techniques in spectral theory and partial differential equations * Offers a complete analysis of the two-dimensional Ginzburg-Landau functional with large kappa in the presence of a magnetic field * Treats the three-dimensional case thoroughly * Includes open problems Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Functional analysis --- Partial differential equations --- Mathematical analysis --- Mathematics --- Thermal properties of solids --- Electronics --- supergeleiding --- differentiaalvergelijkingen --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- elektronica --- micro-elektronica

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While basic features of polarons were well recognized a long time ago and have been described in a number of review papers and textbooks, interest in the role of electron-phonon interactions and polaron dynamics in contemporary materials has recently gone through a vigorous revival. Electron-phonon interactions have been shown to be relevant in high-temperature superconductors and colossal magnetoresistance oxides, and transport through nanowires and quantum dots also often depends on vibronic displacements of ions. The continued interest in polarons extends beyond physical description of advanced materials. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalization, density-matrix renormalization group, dynamic mean-field, and quantum Monte Carlo techniques. Single and multi-polaron theories have offered a new insight in our understanding of high-temperature superconductivity, colossal magnetoresistance, and the correlated transport through molecular quantum dots. This book reviews some recent developments in the field of polarons, starting with the basics and covering a number of active directions of research.

Quantum mechanics. Quantumfield theory --- Optics. Quantum optics --- Statistical physics --- Electromagnetism. Ferromagnetism --- Thermal properties of solids --- Solid state physics --- Matter physics --- Theoretical spectroscopy. Spectroscopic techniques --- Electronics --- supergeleiding --- EMI (electromagnetic interference) --- vaste stof --- materie (fysica) --- quantummechanica --- spectroscopie --- microscopie --- elektrodynamica --- elektronica --- fysica --- micro-elektronica --- optica