Download or read book Some Mathematical Problems in the Ginzburg Landau Theory of Superconductivity written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Mathematical Problems in the Ginzburg Landau Theory of Superconductivity written by Stephen J. Gustafson and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In agreement with the Landau theory of phase transitions, a superconductor is described macroscopically by the Ginzburg-Landau equations (1950). These are nonlinear partial differential equations for a complex-valued function, y (the order parameter), and a vector-field 'A' (the vector potential). The equations contain a parameter, [lambda], which determines whether they describe a superconductor of the first kind ([lambda] 1), or of the second kind ([lambda] 1). It was observed by Abrikosov (1957) that a highly-symmetric family of solutions known as 'n'-vortices plays a central role in the theory. These solutions are classified by their integer topological degree, nZ . The principal goal of this thesis is to establish the stability properties of the 'n'-vortex. The stability question is studied for three types of evolution equations: a gradient flow, a nonlinear wave equation, and a nonlinear Schrödinger equation. Our main result determines the dependence of the stability of 'n'-vortices on the topological degree, 'n', and on the parameter, [lambda]. Specifically, we prove that for [lambda] 1, all vortices are stable, while for [lambda] 1, 'n'-vortices are stable if 'n' = ±1 and unstable if @'n'@ >= 2. Previous work on vortex stability (Taubes (1980), Stuart (1994)) has focused on the special case [lambda] = 1, in which the Ginzburg-Landau equations reduce to the first-order Bogomolnyi equations. In particular, our result resolves a long-standing conjecture, first rigorously formulated by Jaffe and Taubes (1980).
Download or read book Some Mathematical Problems in the Ginzburg Landau Theory of Superconductivity microform written by Stephen J. Gustafson and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 1999 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Connectivity and Superconductivity written by Jorge Berger and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The motto of connectivity and superconductivity is that the solutions of the Ginzburg–Landau equations are qualitatively in?uenced by the topology of the boundaries. Special attention is given to the “zero set”,the set of the positions (usually known as “quantum vortices”) where the order parameter vanishes. The paradigm of connectivity and superconductivity is the Little– Parks e?ect,discussed in most textbooks on superconductivity. This volume is intended to serve as a reference book for graduate students and researchers in physics or mathematics interested in superconductivity, or in the Schr ̈ odinger equation as a limiting case of the Ginzburg–Landau equations. The e?ects considered here usually become important in the regime where the coherence length is of the order of the dimensions of the sample. While in the Little–Parks days a lot of ingenuity was required to achieve this regime, present microelectronic techniques have transformed it into a routine. Mo- over,measurement and visualization techniques are developing at a pace which makes it reasonable to expect veri?cation of distributions,and not only of global properties. Activity in the ?eld has grown and diversi?ed substantially in recent years. We have therefore invited experts ranging from experimental and theoretical physicists to pure and applied mathematicians to contribute articles for this book. While the skeleton of the book deals with superconductivity,micron- works and generalizations of the Little–Parks situation,there are also articles which deal with applications of the Ginzburg–Landau formalism to several fundamental topics,such as quantum coherence,cosmology,and questions in materials science.
Download or read book Ginzburg Landau Phase Transition Theory and Superconductivity written by K.-H. Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.
Download or read book Vortices in the Magnetic Ginzburg Landau Model written by Etienne Sandier and published by Springer Science & Business Media. This book was released on 2008-05-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field.
Download or read book Ginzburg landau Vortices written by Haim Brezis and published by World Scientific. This book was released on 2005-04-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ginzburg-Landau equation as a mathematical model of superconductors has become an extremely useful tool in many areas of physics where vortices carrying a topological charge appear. The remarkable progress in the mathematical understanding of this equation involves a combined use of mathematical tools from many branches of mathematics. The Ginzburg-Landau model has been an amazing source of new problems and new ideas in analysis, geometry and topology. This collection will meet the urgent needs of the specialists, scholars and graduate students working in this area or related areas.
Download or read book Ginzburg Landau Phase Transition Theory and Superconductivity written by Karl-Heinz Hoffmann and published by . This book was released on 2001 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.
Download or read book Nonlinear Dynamics and Renormalization Group written by Israel Michael Sigal and published by American Mathematical Soc.. This book was released on 2001 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathématiques (CRM) in Montréal (Canada), as part of the year-long program devoted to mathematical physics. In the book, active researchers in the fields of nonlinear partial differential equations and renormalization group contribute recent results on topics such as Ginzburg-Landau equations and blow-up of solutions of the nonlinear Schroedinger equations, quantum resonances, and renormalization group analysis in constructive quantum field theory. This volume offers the latest research in the rapidly developing fields of nonlinear equations and renormalization group.
Download or read book Introduction to Superfluidity written by Andreas Schmitt and published by Springer. This book was released on 2014-07-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superfluidity – and closely related to it, superconductivity – are very general phenomena that can occur on vastly different energy scales. Their underlying theoretical mechanism of spontaneous symmetry breaking is even more general and applies to a multitude of physical systems. In these lecture notes, a pedagogical introduction to the field-theory approach to superfluidity is presented. The connection to more traditional approaches, often formulated in a different language, is carefully explained in order to provide a consistent picture that is useful for students and researchers in all fields of physics. After introducing the basic concepts, such as the two-fluid model and the Goldstone mode, selected topics of current research are addressed, such as the BCS-BEC crossover and Cooper pairing with mismatched Fermi momenta.
Download or read book Statistical Mechanics of Superconductivity written by Takafumi Kita and published by Springer. This book was released on 2015-05-05 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on a coherent state in terms of the Cooper-pair creation operator, a quasiparticle field for describing the excitation and the variational principle in statistical mechanics. They have the advantage that the phase coherence due to the Cooper-pair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classic s-wave superconductors and its extension to the p-wave superfluidity of 3He. Later, the mean-field equations are simplified to the Eilenberger and Ginzburg–Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov’s flux-line lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of p-wave superfluidity in liquid 3He. The book serves as a standard reference for advanced courses of statistical mechanics with exercises along with detailed answers.
Download or read book Spectral Methods in Surface Superconductivity written by Søren Fournais and published by Springer Science & Business Media. This book was released on 2010-06-15 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.
Download or read book Spectral Methods in Surface Superconductivity written by Søren Fournais and published by Springer Science & Business Media. This book was released on 2010-05-19 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.
Download or read book Ginzburg Landau Theory of Condensates written by Baruch Rosenstein and published by Cambridge University Press. This book was released on 2021-11-18 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.
Download or read book Modern Aspects Of Superconductivity Theory Of Superconductivity Second Edition written by Sergei Kruchinin and published by World Scientific. This book was released on 2021-04-14 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to superconductivity, which is one of the most interesting problems in physics. In accordance with the outline of the book, it treats the key problems in the field of superconductivity, in particular, it discusses the mechanism(s) of superconductivity. This book is useful for researchers and graduate students in the fields of solid state physics, quantum field theory, and many-body theory.
Download or read book Introduction to Unconventional Superconductivity written by V.P. Mineev and published by CRC Press. This book was released on 1999-09-21 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unconventional superconductivity (or superconductivity with a nontrivial Cooper pairing) is believed to exist in many heavy-fermion materials as well as in high temperature superconductors, and is a subject of great theoretical and experimental interest. The remarkable progress achieved in this field has not been reflected in published monographs and textbooks, and there is a gap between current research and the standard education of solid state physicists in the theory of superconductivity. This book is intended to meet this information need and includes the authors' original results.
Download or read book MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS written by STEPHEN J. GUSTAFSON and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.
