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Some mathematical problems in the ginzburg-landau theory of superconductivity.

Stephen J. Gustafson

Some mathematical problems in the ginzburg-landau theory of superconductivity.

by Stephen J. Gustafson

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Published .
Written in


The Physical Object
Pagination78 leaves.
Number of Pages78
ID Numbers
Open LibraryOL21029286M
ISBN 100612457389

Superconductivity and Ginzburg-Landau theory Stefan K¨olling Universit¨at Bonn Superconductivity is the consequence of an electron-phonon interaction. To proceed we must invoke some approximation, we expect that fluctuations will be smallFile Size: KB.   Macroscopic theory of superconductivity valid for magnetic fields of arbitrary magnitude and the behaviour of superconductors in weak high frequency fields are discussed. The problem of formulating a microscopic theory of superconductivity is also by:

  In the history of superconductivity, another well-known theory, named the Ginzburg–Landau (GL) the has also had an important role. The GL theory gives the phenomenological description of Cited by: 6. The Ginzburg–Landau theory provides a powerful tool for exploring systems with inhomogeneous order parameters near the critical temperature. For instance, its application to the surface energy of a normal-superconducting interface led to the discovery of the two types of by:

Theory of superconductivity (low Tc) Ginzburg & Landau phenomenological theory complex wave function Ψ= ρ eiθ ρ2: density of superconducting carriers . 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 Price: $


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Some mathematical problems in the ginzburg-landau theory of superconductivity by Stephen J. Gustafson Download PDF EPUB FB2

Ginzburg-Landau Phase Transition Theory and Superconductivity (International Series of Numerical Mathematics) Softcover reprint of the original 1st ed. Edition by K.-H. Hoffmann (Author) › Visit Amazon's K.-H.

Hoffmann Page. Find all the books, read about the author, and more. Cited by: In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical physical theory used to describe its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties.

grantor: University of Toronto. TSpace. TSpace is a free and secure research repository established by University of Toronto Libraries to disseminate and preserve the scholarly record of University of by: 2.

SOME bfATHEMATICAL PROBLETVIS IN THE GINZBURG-LANDAU THEORY OF SUPERCONDUCTIVITY Ph-D. Thesis, Stephen J. Gustafson Graduate Department of Mathematics University of Toronto Abstract: In agreement with the Landau theory of phase transitions, a su- perconductor is described macroscopically by the Ginzburg-Landau equations ().Cited by: 2.

today Landau theory, or Landau-Ginzburg theory. Sometimes it is also called Ginzburg-Landau theory, because the two wrote a paper applying these ideas to superconductivity. However, the original insight came from a solo paper of Landau’s in ; Ginzburg later understood how to see what goes wrong with Landau theory, explained below in File Size: KB.

Before ending this discussion, it will be helpful going forward to mention some issues of nomenclature. In the usual Ginzburg-Landau theory, it is (~r) that is taken as the wave function (or order parameter, as it is sometimes called in that theory), because, as we shall see, File Size: 2MB. () Global well-posedness of the time-dependent Ginzburg–Landau superconductivity model in curved polyhedra.

Journal of Mathematical Analysis and Applications() Directed motion of vortices and annihilation of vortex–antivortex pairs in finite-gap superconductors via hot-lattice by: The theory of complex Ginzburg-Landau type phase transition and its applica­ tions to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continuously and persistently studied since the s.

Today, there is an abundance of mathematical results spread over numer­ ous scientific journals. A series of lectures on superconductivity. Courtesy of Professor Bartek Glowaki of the University of Cambridge, who filmed, directed and edited the videos. This particular talk is about the. Vortices in the Ginzburg–Landau model of superconductivity Sylvia Serfaty Abstract.

We review some mathematical results on the Ginzburg–Landau model with and without magnetic field. The Ginzburg–Landau energy is the standard model for superconduc-tivity, able to predict the existence of vortices (which are quantized, topological defects) in. Theory of Superconductivity. This note covers the following topics: Topology and Geometry for Physics, The Fundamentals of Density Functional Theory, The Particle World of Condensed Matter, Theory of Superconductivity: A Primer, Microscopic Theory of Superconductivity, The Essentials of DFT and FPLO, High Tc Superconductors: Electronic structure, BCS(Beschreibung des supraleitenden Zustands.

6 Ginzburg-Landau Theory 34 Superconductivity is due to an effective attraction between conduction electrons. Since two electrons experience a re-pulsive Coulomb force, there must be an additional attrac- In some ma-terials, then, the second term might “win” at low frequencies, depending on details.

The BCS interaction is sometimes re-File Size: KB. Superconductivity: Ginzburg-Landau Theory Some of the key ideas for the Landau mean field description of phase transitions were developed in the context of superconductivity. It turns out that for conventional (low-Tc) superconductors, mean field theoryFile Size: 61KB.

the dynamic models, i.e., the time-dependent Ginzburg–Landau TDGL equations were subse-quently made,31 Since then, many other works have appeared in the literature, including the development of different types of numerical approximations of Ginzburg–Landau-type models, their rigorous theoretical analysis as well as extensive simulations.

Get this from a library. Ginzburg-Landau phase transition theory and superconductivity. [K -H Hoffmann; Q Tang] -- The theory of complex Ginzburg-Landau type phase transition and its applications to superconductivity and superfluidity has been a topic of great interest to.

The book is meant to provide an authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.\/span>\"@ en\/a> ; \u00A0\u00A0\u00A0\n schema:description\/a> \" 1 Introduction -- Brief history -- The G-L.

The time-dependent Ginzburg-Landau model of superconductivity is examined in the high-x, high magnetic field setting. This work generalizes the previous result for the steady-state model with a. theory of superconductivity was one of the hardest problems in physics of the 20th century.

In light of the topic of this article, it is not without a sense of irony that the original discovery by Kamerlingh Onnes seems to have been motivated, at least in part, by an incorrect theory itself, proposed by another highly influential by: () The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem.

Annales de l'Institut Henri Poincare (C) Non Linear Analysis() Motion and Homogenization of Vortices in Anisotropic Type II by: Introduction to The Theory of Superconductivity (PDF 82P) This note covers the following topics: introduction, superconducting transition, the london model, meissner effect, phase coherence, magnetic flux quantization, coherence length and the energy gap, critical currents and magnetic fields, condensation energy, critical currents, quantized vortices, basic concepts, vortices in the.

We review some mathematical results on the Ginzburg Landau model with and without magnetic field. The Ginzburg Landau energy is the standard model for superconductivity, able to predict the Author: Sylvia Serfaty.conceptual and mathematical foundation for conventional superconductivity, the Bardeen-Cooper-Schrie er (BCS) theory, for which they later received the Nobel Prize for in We will look at features of superconductors before the discovery of the BCS theory, and examine the assump-tions and methods used to develop the theory.

We willFile Size: KB.6 Ginzburg-Landau theory 30 course is dealing with the theory of superconductivity. We want to understand superconductivity using methods of theoretical physics. Experiments will be mentioned if they motivate certain theoretical ideas or support or peratures low enough to achieve superconductivity in some chemical elements.

Inhe File Size: KB.