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Some Mathematical Problems In The Ginzburg Landau Theory Of Superconductivity
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Book Synopsis Ginzburg-Landau Phase Transition Theory and Superconductivity by : K.-H. Hoffmann
Download or read book Ginzburg-Landau Phase Transition Theory and Superconductivity written by K.-H. Hoffmann and published by Nelson Thornes. This book was released on 2001 with total page 442 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.
Book Synopsis Nonlinear Dynamics and Renormalization Group by : Israel Michael Sigal
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.
Book Synopsis On Superconductivity and Superfluidity by : Vitaly L. Ginzburg
Download or read book On Superconductivity and Superfluidity written by Vitaly L. Ginzburg and published by Springer Science & Business Media. This book was released on 2008-11-20 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Nobel Laureate presents his view of developments in the field of superconductivity, superfluidity and related theory. The book contains Ginzburg’s amended version of the Nobel lecture in Physics 2003, as well as his expanded autobiography.
Book Synopsis Vortices in the Magnetic Ginzburg-Landau Model by : Etienne Sandier
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.
Book Synopsis Introduction to Superfluidity by : Andreas Schmitt
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.
Book Synopsis Ginzburg-Landau Vortices by : Fabrice Bethuel
Download or read book Ginzburg-Landau Vortices written by Fabrice Bethuel and published by Birkhäuser. This book was released on 2017-09-21 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.
Book Synopsis Introduction to Unconventional Superconductivity by : V.P. Mineev
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.
Book Synopsis Spectral Methods in Surface Superconductivity by : Søren Fournais
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.
Book Synopsis Nonlinear Partial Differential Equations in Geometry and Physics by : Garth Baker
Download or read book Nonlinear Partial Differential Equations in Geometry and Physics written by Garth Baker and published by Birkhäuser. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.
Book Synopsis Modern Aspects Of Superconductivity: Theory Of Superconductivity (Second Edition) by : Sergei Kruchinin
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.
Book Synopsis MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS by : STEPHEN J. GUSTAFSON
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.
Book Synopsis Statistical Mechanics of Superconductivity by : Takafumi Kita
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.
Book Synopsis Sobolev Spaces in Mathematics III by : Victor Isakov
Download or read book Sobolev Spaces in Mathematics III written by Victor Isakov and published by Springer Science & Business Media. This book was released on 2008-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, marking the centenary of S.L. Sobolev’s birth, presents the latest the results on some important problems of mathematical physics. The book contains two short biographical articles and unique archive photos of S. Sobolev.
Book Synopsis CRM Proceedings & Lecture Notes by :
Download or read book CRM Proceedings & Lecture Notes written by and published by . This book was released on 1993 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Collection of Papers on Geometry, Analysis and Mathematical Physics by : Daqian Li
Download or read book Collection of Papers on Geometry, Analysis and Mathematical Physics written by Daqian Li and published by World Scientific. This book was released on 1997 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics ? the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of ?Gu Chaohao and I? written by C N Yang, ?The academic career and accomplishment of Professor Gu Chaohao? by T T Li and ?List of publications of Professor Gu Chaohao?.
Book Synopsis Theory Of Superconductivity by : J. Robert Schrieffer
Download or read book Theory Of Superconductivity written by J. Robert Schrieffer and published by CRC Press. This book was released on 2018-03-05 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Superconductivity is primarily intended to serve as a background for reading the literature in which detailed applications of the microscopic theory of superconductivity are made to specific problems.
Book Synopsis Numerical Mathematics by : Günther Hämmerlin
Download or read book Numerical Mathematics written by Günther Hämmerlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In truth, it is not knowledge, but learning, not possessing, but production, not being there, but travelling there, which provides the greatest pleasure. When I have completely understood something, then I turn away and move on into the dark; indeed, so curious is the insatiable man, that when he has completed one house, rather than living in it peacefully, he starts to build another. " Letter from C. F. Gauss to W. Bolyai on Sept. 2, 1808 This textbook adds a book devoted to applied mathematics to the series "Grundwissen Mathematik. " Our goals, like those of the other books in the series, are to explain connections and common viewpoints between various mathematical areas, to emphasize the motivation for studying certain prob lem areas, and to present the historical development of our subject. Our aim in this book is to discuss some of the central problems which arise in applications of mathematics, to develop constructive methods for the numerical solution of these problems, and to study the associated questions of accuracy. In doing so, we also present some theoretical results needed for our development, especially when they involve material which is beyond the scope of the usual beginning courses in calculus and linear algebra. This book is based on lectures given over many years at the Universities of Freiburg, Munich, Berlin and Augsburg.
