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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.

Differential equations, Partial. --- Electronic books. -- local. --- Spectral theory (Mathematics). --- Superconductivity --- Spectral theory (Mathematics) --- Differential equations, Partial --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Electricity & Magnetism --- Partial differential equations --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Partial differential equations. --- Special functions. --- Superconductivity. --- Superconductors. --- Electronics. --- Microelectronics. --- Analysis. --- Functional Analysis. --- Electronics and Microelectronics, Instrumentation. --- Strongly Correlated Systems, Superconductivity. --- Partial Differential Equations. --- Special Functions. --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Global analysis (Mathematics). --- Differential equations, partial. --- Functions, special. --- Special functions --- Mathematical analysis --- Electrical engineering --- Physical sciences --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Electric conductivity --- Critical currents --- Superfluidity --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- 517.1 Mathematical analysis --- Materials

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There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes and the Morse inequalities.

Differential geometry. Global analysis --- Partial differential equations --- Quantum mechanics. Quantumfield theory --- Statistical physics --- Engineering sciences. Technology --- differentiaalvergelijkingen --- quantumfysica --- statistische kwaliteitscontrole --- industriële statistieken --- differentiaal geometrie

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Operator theory

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Equations aux derivees partielles elliptiques --- Equations aux derivees partielles hypoelliptiques

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