By Jorge Berger, Jacob Rubinstein

"The motto of connectivity and superconductivity is that the ideas of the Ginzburg-Landau equations are qualitatively encouraged 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 results thought of the following frequently turn into vital within the regime the place the coherence size is of the order of the scale of the pattern. It takes the instinct of physicists and the attention of mathematicians to discover those new results. In Connectivity and Superconductivity, theoretical and experimental physicists are introduced including natural and utilized mathematicians to check those excellent results.This quantity is meant to function a reference e-book for graduate scholars and researchers in physics or arithmetic attracted to superconductivity, or within the Schrodinger equation as a proscribing 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, important Bruyndoncx, Lieve Van glance -- 0 set of the order parameter, specifically in earrings / Jorge Berger -- continual currents in Ginzburg-Landau versions / Luís Almeida, Fabrice Bethuel -- at the normal/superconducting section transition within the presence of huge 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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E. their connectivity) than to their geometry. To study this kind of system in the vicinity of the normal-superconductor transition, de Gennes devised the theory which we are going to present below. The importance of percolation phenomena in this systems lead Shlomo Alexander [1,3] in 1983 to the study of certain systems which are paradigmatic in percolation theory, like the so called Sierpinsky gasket. The possibility of building regular superconducting networks lead other authors to the study of these latter structures, as models of artiﬁcial systems in which quantum coherence plays an important role [12,23,25,26] due to ﬂuxoid quantization along intertwined loops.

At a given point of coordinate s on a branch we take A =A(s)s, s being the unit vector directed along the branch at that point. Near the phase transition boundary , ψ → 0, j →0 and A → Ae , where Ae is the externally applied magnetic potential at the transition. 15) is the sum over all branches. In this expression, ψ(s) is the only quantity to be determined variationally. 17) is the sum over the branches connecting the node a with its ﬁrst neighbor nodes a . This conditions imply the validity of Kirchhoﬀ laws at each node.

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. The present review is dedicated to a presentation of the bibliography and the more relevant results referred to superconducting micronetworks, that is to say, circuits made of superconducting material, fabricated by photolitography or carved using particle beams, electrons or ions, on insulating substrates.