Amorphous solids: their structure, lattice dynamics and elasticity

Using the complete nonlinear Ginzburg-Landau theory, we investigated the superconducting state and phase boundaries for mesoscopic square samples containing one to four submicron antidots in the presence of a uniform perpendicular magnetic field. The properties of the different vortex states, possible degeneracies, and the transitions between them are studied. Due to the interplay of the different types of symmetry, a qualitative difference in the nucleation of the superconducting state in samples with different number or arrangement of antidots is found. The superconducting/normal state $H\ensuremath{-}T$ phase boundary of these structures reveals an oscillatory behavior caused by the formation of different stable vortex configurations in these small clusters of pinning centers (antidots). We analyze the stability of these configurations and compare the superconducting phase boundary with experimental results.

Stability and transition between vortex configurations in square mesoscopic samples with antidots

This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly infinite) union of one-dimensional intervals and a totally disconnected (possibly uncountable) compact set, which roughly speaking represents the set of junction points. Classical quantum graphs and fractal spaces such as the Hanoi attractor are included among them. We begin with proving the existence of a resistance form on the Hanoi attractor, and go on to establish heat kernel estimates and upper and lower bounds on the eigenvalue counting function of Laplacians corresponding to weakly self-similar measures on the Hanoi attractor. These estimates and bounds rely heavily on the relation between the length and volume scaling factors of the fractal. We then state and prove a necessary and sufficient condition for the existence of a resistance form on a general fractal quantum graph. Finally, we extend our spectral results to a large class of weakly self-similar fractal quantum graphs.

Energy and Laplacian on Hanoi-type fractal quantum graphs

The authors present, after a recent determination of the transfer integrals at low temperature in (TMTCF)2X salts, the band structure and the Fermi surface of these compounds. Changes in the optimal nesting vector upon cooling are discussed.

Temperature dependence of the Fermi surface topography in the (TOTSF)2X and (TMTTF)2X families

This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly infinite) union of 1-dimensional intervals and a totally disconnected (possibly uncountable) compact set, which roughly speaking represents the set of junction points. Classical quantum graphs and fractal spaces such as the Hanoi attractor are included among them. We begin with proving the existence of a resistance form on the Hanoi attractor, and go on to establish heat kernel estimates and upper and lower bounds on the eigenvalue counting function of Laplacians corresponding to weakly self-similar measures on the Hanoi attractor. These estimates and bounds rely heavily on the relation between the length and volume scaling factors of the fractal. We then state and prove a necessary and sufficient condition for the existence of a resistance form on a general fractal quantum graph. Finally, we extend our spectral results to a large class of weakly self-similar fractal quantum graphs.

2014 The magnetic energies and critical fields of networks of thin wires are calculated for the square net and the Sierpinski gasket and the results are applied to percolation clusters. The results are obtained by a systematic expansion of the Landau Ginzburg equations around the constant amplitude London limit. The role of flux quantization and local critical currents are included in a systematic way. For percolation we assume a short distance self similar fractal structure of the clusters with proper crossovers and inclusion of the Stauffer cluster distribution. Simple scaling forms for the magnetic energy and for the superconducting coherence length, and for the critical field of finite clusters and of the infinite cluster are obtained. The results are compared with other studies of the same problem and the origin of the discrepancies is discussed. We also discuss existing experiments and suggest some new experimental approaches. J. Physique 44 (1983) 805-817 JUILLET 1983, Classification Physics Abstracts 74.30 05.40

E. Halevi

Papers

Superconductivity on networks : II. The London approach