By Jorge Berger, Jacob Rubinstein
"The motto of connectivity and superconductivity is that the strategies of the Ginzburg-Landau equations are qualitatively motivated by means of the topology of the bounds, as in multiply-connected samples. specific attentions is paid to the "zero set", the set of positions (usually referred to as "quantum vortices") the place the order parameter vanishes. the consequences thought of right here frequently develop into vital within the regime the place the coherence size is of the order of the size of the pattern. It takes the instinct of physicists and the notice of mathematicians to discover those new results. In Connectivity and Superconductivity, theoretical and experimental physicists are introduced including natural and utilized mathematicians to study those remarkable results.This quantity is meant to function a reference booklet for graduate scholars and researchers in physics or arithmetic attracted to superconductivity, or within the Schrodinger equation as a restricting case of the Ginzburg-Landau equations."--BOOK JACKET. learn more... within the reminiscence of Shlomo Alexander / Pierre-Gilles de Gennes -- Topological issues in superconductivity / Jacob Rubinstein -- The de Gennes-Alexander idea of superconducting micronetworks / José I. Castro, Arturo López -- Nodal units, multiplicity and superconductivity in non-simply attached domain names / Bernard Helffer ... [et al.] -- Connectivity and flux confinement phenomena in nanostructured superconductors / Victor V. Moshchalkov, very important Bruyndoncx, Lieve Van glance -- 0 set of the order parameter, specifically in jewelry / Jorge Berger -- continual currents in Ginzburg-Landau versions / Luís Almeida, Fabrice Bethuel -- at the normal/superconducting section transition within the presence of enormous magnetic fields / Peter Sternberg -- at the numerical answer of the time-dependent Ginzburg-Landau equations in multiply hooked up domain names / Gustavo C. Buscaglia, Carlos Bolech, Arturo López -- Formation of vortex-antivortex pairs / Sanatan Digal ... [et al.] -- The order parameter as a macroscopic quantum wavefunction / Antony J. Leggett -- The Ehrenberg-Siday-Aharonov-Bohm impression / Charles G. Kuper -- Connectivity and superconductivity in inhomogeneous buildings / man Deutscher
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Additional info for Connectivity and superconductivity
Denoting the primitive of A by ζ, our choice of M guarantees that eiζ is a single valued function on M . This is the crucial observation that facilitates the analysis. It is here that we need the condition that the ﬂux through every cycle of M is an odd integer times π. We can therefore deﬁne the new gauge v = e−iζ ψ. 48) where we introduced a weight w that models nonuniformities in the network thickness. The nonuniformity will enable us to investigate symmetry breaking even in single loops. Consider further the mapping G : M → M which sends every point to its corresponding point on the other copy of M .
Later on several papers applied the theoretical formulation developed by de Gennes and Alexander to micronetworks of varied geometric and topological characteristics (inﬁnite networks, planar and spaJ. Berger and J. ): LNP m62, pp. 23–62, 2000. c Springer-Verlag Berlin Heidelberg 2000 24 J. I. Castro and A. ) obtaining results which are important not only because of the physics underlying them but also because of possible future applications. The de Gennes-Alexander theory was very successful in explaining the description of the second order phase transition between the normal and superconducting phases and is the subject of this review.
This is the crucial observation that facilitates the analysis. It is here that we need the condition that the ﬂux through every cycle of M is an odd integer times π. We can therefore deﬁne the new gauge v = e−iζ ψ. 48) where we introduced a weight w that models nonuniformities in the network thickness. The nonuniformity will enable us to investigate symmetry breaking even in single loops. Consider further the mapping G : M → M which sends every point to its corresponding point on the other copy of M .