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A Ginzburg Biography & Facts
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. One GL-type superconductor is the famous YBCO, and generally all cuprates.Later, a version of Ginzburg–Landau theory was derived from the Bardeen–Cooper–Schrieffer microscopic theory by Lev Gor'kov, thus showing that it also appears in some limit of microscopic theory and giving microscopic interpretation of all its parameters. The theory can also be given a general geometric setting, placing it in the context of Riemannian geometry, where in many cases exact solutions can be given. This general setting then extends to quantum field theory and string theory, again owing to its solvability, and its close relation to other, similar systems. Introduction Based on Landau's previously established theory of second-order phase transitions, Ginzburg and Landau argued that the free energy density fs{\displaystyle f_{s}} of a superconductor near the superconducting transition can be expressed in terms of a complex order parameter field ψ(r)=|ψ(r)|eiϕ(r){\displaystyle \psi (r)=|\psi (r)|e^{i\phi (r)}}, where the quantity |ψ(r)|2{\displaystyle |\psi (r)|^{2}} is a measure of the local density of superconducting electrons ns(r){\displaystyle n_{s}(r)} analogous to a quantum mechanical wave function. While ψ(r){\displaystyle \psi (r)} is nonzero below a phase transition into a superconducting state, no direct interpretation of this parameter was given in the original paper. Assuming smallness of |ψ|{\displaystyle |\psi |} and smallness of its gradients, the free energy density has the form of a field theory and exhibits U(1) gauge symmetry: where fn{\displaystyle f_{n}} is the free energy density of the normal phase, α(T){\displaystyle \alpha (T)} and β(T){\displaystyle \beta (T)} are phenomenological parameters that are functions of T (and often written just α{\displaystyle \alpha } and β{\displaystyle \beta }). m∗{\displaystyle m^{*}} is an effective mass, e∗{\displaystyle e^{*}} is an effective charge (usually 2e{\displaystyle 2e}, where e is the charge of an electron), A{\displaystyle \mathbf {A} } is the magnetic vector potential, and B=∇×A{\displaystyle \mathbf {B} =\nabla \times \mathbf {A} } is the magnetic field.The total free energy is given by F=∫fsd3r{\displaystyle F=\int f_{s}d^{3}r}. By minimizing F{\displaystyle F} with respect to variations in the order parameter ψ{\displaystyle \psi } and the vector potential A{\displaystyle \mathbf {A} }, one arrives at the Ginzburg–Landau equations where J{\displaystyle J} denotes the dissipation-free electric current density and Re the real part. The first equation — which bears some similarities to the time-independent Schrödinger equation, but is principally different due to a nonlinear term — determines the order parameter, ψ{\displaystyle \psi }. The second equation then provides the superconducting current. Simple interpretation Consider a homogeneous superconductor where there is no superconducting current and the equation for ψ simplifies to: This equation has a trivial solution: ψ = 0. This corresponds to the normal conducting state, that is for temperatures above the superconducting transition temperature, T > Tc. Below the superconducting transition temperature, the above equation is expected to have a non-trivial solution (that is ψ≠0{\displaystyle \psi \neq 0}). Under this assumption the equation above can be rearranged into: When the right hand side of this equation is positive, there is a nonzero solution for ψ (remember that the magnitude of a complex number can be positive or zero). This can be achieved by assuming the following temperature dependence of α:α(T)=α0(T−Tc){\displaystyle \alpha :\alpha (T)=\alpha _{0}(T-T_{\rm {c}})} with α0/β>0{\displaystyle \alpha _{0}/\beta >0}: Above the superconducting transition temperature, T > Tc, the expression α(T) / β is positive and the right hand side of the equation above is negative. The magnitude of a complex number must be a non-negative number, so only ψ = 0 solves the Ginzburg–Landau equation. Below the superconducting transition temperature, T < Tc, the right hand side of the equation above is positive and there is a non-trivial solution for ψ. Furthermore, that is ψ approaches zero as T gets closer to Tc from below. Such a behavior is typical for a second order phase transition.In Ginzburg–Landau theory the electrons that contribute to superconductivity were proposed to form a superfluid. In this interpretation, |ψ|2 indicates the fraction of electrons that have condensed into a superfluid. Coherence length and penetration depth The Ginzburg–Landau equations predicted two new characteristic lengths in a superconductor. The first characteristic length was termed coherence length, ξ. For T > Tc (normal phase), it is given by ξ=ℏ22m∗|α|.{\displaystyle \xi ={\sqrt {\frac {\hbar ^{2}}{2m^{*}|\alpha |}}}.}while for T < Tc (superconducting phase), where it is more relevant, it is given by ξ=ℏ24m∗|α|.{\displaystyle \xi ={\sqrt {\frac {\hbar ^{2}}{4m^{*}|\alpha |}}}.}It sets the exponential law according to which small perturbations of density of superconducting electrons recover their equilibrium value ψ0. Thus this theory characterized all superconductors by two length scales. The second one is the penetration depth, λ. It was previously introduced by the London brothers in their London theory. Expressed in terms of the parameters of Ginzburg–Landau model it is λ=m∗μ0e∗2ψ02=m∗βμ0e∗2|α|,{\displaystyle \lambda ={\sqrt {\frac {m^{*}}{\mu _{0}e^{*2}\psi _{0}^{2}}}}={\sqrt {\frac {m^{*}\beta }{\mu _{0}e^{*2}|\alpha |}}},}where ψ0 is the equilibrium value of the order parameter in the absence of an electromagnetic field. The penetration depth sets the exponential law according to which an external magnetic field decays inside the superconductor. The original idea on the parameter κ belongs to Landau. The ratio κ = λ/ξ is presently known as the Ginzburg–Landau parameter. It has been proposed by Landau that Type I superconductors are those with 0 < κ < 1/√2, and Type II superconductors those with κ > 1/√2. Fluctuations The phase transition from the normal state is of second order for Type II superconductors, taking into account fluctuations, as demonstrated by Dasgupta and Halperin, while for Type I superconductors it is of first order, as demonstrated by Halperin, Lubensky and Ma. Classification of superconductors In the original paper Ginzburg and Landau observed the existence of two types of superconductors depending on the energy of the interface between the normal and superconducting states. The Meissner state breaks down when the applied magnetic field is too large. Superconduc.... 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Lessons in Critical Theory
Robin Myers & Carlos Antonio Aguirre RojasContemporary critical thinking was founded by Karl Marx approximately a century and a half ago. Later, in the twentieth and twentyfirst centuries, various critical thinkers (some M...
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Guerra e pace
Lev TolstojLa piú autentica epopea narrativa della letteratura moderna. Sullo sfondo della crisi europea degli inizi dell'Ottocento, si intrecciano le vicende dei membri di due famiglie dell'...
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Anna Karenina
Lev TolstojUna storia travolgente di grande passione e trasgressione, di sguardi incrociati, voti traditi, drammi coniugali, slanci romantici, ideali infranti, verità ultime. A oltre settant'...
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The Ties That Bind
Tesni MorganAn amoral and unprincipled but charismatic and goodlooking young man calling himself Jack turns up to a Halloween party dressed as the Devil. The lady of the house is Kim Buckley...
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Lydia In The Harem
Philippa MastersThe Boer War has erupted in Africa and Lydia must sail for England. She looks forward to her voyage with a crew of lusty mariners. When the ship is forced to dock in Arabia, a Prin...
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The Soul of a Shoemaker
Susan CorkA Shoemaker struggles to survive in an oppressed society. Can he outsmart the brutal regime before he becomes the next victim? In 1950s Yugoslavia, master cobbler Frank Katana m...
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Coventry
Rachel CuskNPR's Favorite Books of 2019Rachel Cusk redrew the boundaries of fiction with the Outline Trilogy, three “literary masterpieces” (The Washington Post) whose narrator, Faye, perceiv...
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Vortices in the Magnetic Ginzburg-Landau Model
Etienne Sandier & Sylvia SerfatyWith the discovery of typeII superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object ...
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Elinor Guggenheimer v. Ralph Ginzburg
Court of Appeals of New York[43 N.Y.2d 268 Page 271] Opinion OF THE COURT Noah Webster, whose name in this country became synonymous with the word dictionary, completed his American Dictionary of the English...
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Jacques the Fatalist
Denis Diderot & Michael HenryDenis Diderot (17131784) was among the greatest writers of the Enlightenment, and in Jacques the Fatalist he brilliantly challenged the artificialities of conventional French ficti...
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Natalia Ginzburg
Maria Antonietta Grignani & AA.VV.Natalia Ginzburg ha cambiato le modalità di narrare la memoria: molti dei suoi libri, come Lessico Famigliare e Le piccole virtù, sono un’autobiografia che però resta apparentement...
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Great Italian Stories
Various Authors & Jhumpa LahiriThis handpicked selection from The Penguin Book of Italian Short Stories celebrates the best twentiethcentury literature from Italy.From a mystifying tale of the supernatural to a ...
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Offene Fragen
Vivian GornickDie Grande Dame der amerikanischen Essayistik empfiehlt: Lasst Bücher in euer Leben – und lest sie immer wieder!Für die preisgekrönte Journalistin Vivian Gornick sind Bücher Lebens...
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The Manzoni Family
Natalia Ginzburg & Tim ParksWinner of the Bagutta Prize, The Manzoni Family set in ducal Italy and postrevolutionary France, captures the story of Alessandro Manzonicelebrated Milanese nobleman, man of letter...
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Il giocatore
Fyodor DostoyevskyDivorato da un'insana passione per l'ambigua Polina che sembra non ricambiarlo, il giovane Aleksej si lascia sedurre dal demone del gioco, che lo trascina fatalmente verso una prog...
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The Complete Short Stories of Natalia Ginzburg
Natalia Ginzburg & Paul LewisNatalia Ginzburg (19161991) is today recognized as one of the foremost woman writers to emerge from twentiethcentury Italy. The Complete Short Stories of Natalia Ginzburg brings to...
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The Essential Kerner Commission Report
Jelani Cobb & Matthew GuarigliaRecognizing that an historic study of American racism and police violence should become part of today’s canon, Jelani Cobb contextualizes it for a new generation.The Kerner Commiss...
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The City and the House
Natalia GinzburgThe city is Rome, the hub of Italian life and culture. The house is Le Margherite, a home where the sprawling cast of The City and the House is welcome. At the center of this lush ...
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Der Geist von Turin
Maike AlbathIn Mussolinis Italien, im Schatten der Fabriken von Fiat und Olivetti, begegneten sich in den dreißiger Jahren in Turin ein paar gebildete junge Leute. Sie gründeten Zeitschrifte...
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Voices in the Evening
Natalia Ginzburg & D.M LowFrom one of Italy’s greatest writers, a stunning novel “filled with shimmering, risky, darting observation” (Colm Tóibín) After WWII, a small Italian town struggles to emerge from ...
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The Wrong Door
Wendell RickettsThe Wrong Door is the first Englishlanguage translation of the complete plays of Italian writer Natalia Ginzburg (19161991). Bringing together the eleven plays Ginzburg wrote betwe...
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La corsara
Sandra PetrignaniDalla nascita palermitana alla formazione torinese, fino al definitivo trasferimento a Roma, Sandra Petrignani ripercorre la vita di una grande protagonista del panorama culturale ...
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The Little Virtues
Natalia Ginzburg, Dick Davis & Belle BoggsIn this collection of her finest and bestknown short essays, Natalia Ginzburg explores both the mundane details and inescapable catastrophes of personal life with the grace and wit...
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Representation Theory and Algebraic Geometry
Vladimir Baranovsky, Nicolas Guay & Travis SchedlerThe chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two ...
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Las tareas de casa y otros ensayos
Natalia GinzburgLas lúcidas reflexiones de Natalia Ginzburg, una de las escritoras italianas más importantes del siglo XX. «Me mostró el camino.»Vivian GornickLa soledad de la infancia y los pecad...
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Natalia Ginzburg
Angela M. Jeannet & Giuliana S. KatzA prominent and prolific Italian writer, Natalia Ginzburg (19161991) is known for her novels, plays, short stories, and essays. This collection brings together, for an Englishspeak...
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Die Freibeuterin
Sandra PetrignaniPorträt der großen europäischen Schriftstellerin und Intellektuellen im Spiegel des 20. Jahrhunderts.Sie war eine der bedeutendsten Frauen der europäischen Kulturgeschichte: Natali...
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Vita di Leone Ginzburg
Florence Mauro«Le lascio immaginare il senso di malinconia e di rabbia che mi dà il continuare a essere considerato straniero nel mio paese».Così scriveva Leone Ginzburg, il 1° agosto 1943, all’...
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Der Morgenstern
Karl Ove KnausgårdEs ist Sommer in Norwegen. Eigentlich eine beschauliche, sonnengetränkte Zeit. Doch nun scheint etwas aus den Fugen geraten zu sein. Krabben spazieren an Land, Ratten tauchen an üb...
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Democracy
Henry AdamsAn instant bestseller when first published in 1880, Democracy is the quintessential American political novel. At its heart is Madeleine Lee, a young widow who comes to Washington, ...
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The Little Virtues
Natalia Ginzburg“As far as the education of children is concerned,” states Natalia Ginzburg in this collection of her finest and bestknown short essays, “I think they should be taught not the litt...
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Streghe, sciamani, visionari
Cora PresezziEsito di un lungo e tortuoso percorso di ricerca, Storia notturna è il capolavoro che Carlo Ginzburg ha consacrato al tentativo di spiegare la genesi storica dello stereotipo del s...
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Le Fil et les traces de Carlo Ginzburg
Encyclopaedia UniversalisBienvenue dans la collection Les Fiches de lecture d’UniversalisL'historien écrit ce qui s'est passé. Mais précisément, dans son effort d'écriture, ne se rapprochetil pas trop de l...
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The Manzoni Family
Natalia Ginzburgrich story of passions, writing, rivalries, deaths, and war.Set in ducal Italy and postrevolutionary France, The Manzoni Family tells a rich story of passions, writing, rivalries,...