By Jorge Berger, Jacob Rubinstein

"The motto of connectivity and superconductivity is that the options of the Ginzburg-Landau equations are qualitatively prompted through the topology of the limits, as in multiply-connected samples. distinctive 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 the following frequently develop into very important 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 excellent results.This quantity is meant to function a reference e-book for graduate scholars and researchers in physics or arithmetic drawn 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 concerns 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, specially in earrings / Jorge Berger -- continual currents in Ginzburg-Landau types / Luís Almeida, Fabrice Bethuel -- at the normal/superconducting section transition within the presence of huge magnetic fields / Peter Sternberg -- at the numerical resolution 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 constructions / man Deutscher

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The coherence length ξ and the penetration depth λ are the characteristic distances for changes in the ﬁelds ψ and A respectively. 9) 26 J. I. Castro and A. L´ opez is generally assumed, λ(0) being a constant expressed in terms of the normal state electronic parameters. 11) are quantities independent of T in this theory; the dimensionless ratio κ is usually called the “GL constant”. 7) must be solved with the boundary conditions following from the variational procedure applied to the free energy functional FGL .

C|}. 45) we see at once that the minimizers are periodic with respect to each Φl with a (non-dimensional) period of 2π. This is of course well known experimentally. If the matrix (B T ΛB)−1 is diagonal, then when there are no zeros, for any value of Λ the energy is minimized when every ξl2 is minimized. Therefore each Nl is the closest integer to Φl /2π. This is the case, for example, when every edge of M is a closed loop. For arbitrary M , however, the determination of the {Nl } cannot be decoupled from the amplitude equations.

Bruynseraede, R. Jonckheere: Phys. Rev. B 54, R12701 (1996) 33. M. Tinkham: Introduction to Superconductivity, McGraw Hill, 1996. 34. B. White: Acta Math. 160, 1 (1988) 35. X. C. Price: Phys. Rev. B 55 3128 (1997) 2 The de Gennes–Alexander Theory of Superconducting Micronetworks Jos´e I. 1 Introduction The technology of the second half of the XX century was largely based on the applications of the quantum physics of the solid state, which explains the electronic properties of matter. Technology of the XXI century will surely be based on the macroscopic quantum properties of matter, that is to say, on the coherent macroscopic states of physical systems, some of their best known examples are the laser, superﬂuidity and superconductivity.