By improving resolution of home-made mutual-inductance measurements technique, a pronounced step-like structure (with the number of steps n = 4 for all AC fields) has been observed in the temperature dependence of AC susceptibility in artificially prepared two-dimensional Josephson Junction Arrays (2D-JJA) of unshunted N b − AlOx − N b junctions with βL(4.2K) = 30. Using a single-plaquette approximation of the overdamped 2D-JJA model, we were able to successfully fit our data assuming that steps are related to the geometric properties of the plaquette. The number of steps n corresponds to the number of flux quanta that can be screened by the maximum critical current of the junctions. The steps are predicted to manifest themselves in arrays with the inductance related parameter βL(T ) matching a "quantization" condition βL(0) = 2π(n + 1). PACS: 74.25.Ha, 74.50.+r, 74.80.Bj 1. Introduction. Many unusual and still not completely understood magnetic properties of Josephson Junction Arrays (JJAs) continue to attract attention of both theoreticians and experimentalists alike (for recent reviews on the subject see, e.g. [1,2,3,4] and further references therein). In particular, among the numerous spectacular phenomena recently discussed and observed in JJAs we would like to mention the dynamic temperature reentrance of AC susceptibility [2] (closely related to paramagnetic Meissner effect [3]) and avalanche-like magnetic field behavior of magnetization [4,5] (closely related to self-organized criticality (SOC) [6,7]). More specifically, using highly sensitive SQUID magnetometer, magnetic field jumps in the magnetization curves associated with the entry and exit of avalanches of tens and hundreds of fluxons were clearly seen in SIS-type arrays [5]. Besides, it was shown that the probability distribution of these processes is in good agreement with the SOC theory [7]. An avalanche character of flux motion was observed at temperatures at which the size of the fluxons did not exceed the size of the cell, that is, for discrete vortices. On the other hand, using a similar technique, magnetic flux avalanches were not observed in SNS-type proximity arrays [8] despite a sufficiently high value of the inductance L related critical parameter β L = 2πLI C /Φ 0 needed to satisfy the observability conditions of SOC. Instead, the observed quasi-hydrodynamic flux motion in the array was explained by the considerable viscosity characterizing the vortex motion through the Josephson junctions.

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Colossal negative magnetoresistance ∆ρ(T, B) = ρ(T, B)− ρ(T, 0) observed in La0.6Y0.1Ca0.3M nO3 at B = 1T shows a nearly perfect symmetry around T0 = 160K suggesting a universal field-induced transport mechanism in this material. Attributing this symmetry to strong magnetic fluctuations (triggered by the Y substitution and further enhanced by magnetic field, both above and below the field-dependent Curie temperature TC(B) ≡ T0), the data are interpreted in terms of the nonthermal spin hopping and magnetization M dependent charge carrier localization scenario leading to ∆ρ = −ρs 1 − e −γM 2 with M (T, B) = CB/|T − TC| ν . The separate fits through all the data points above and below TC yield C + ≃ C − and ν + ≃ ν − ≃ 1. The obtained results corroborate the importance of fluctuation effects in this material recently found to dominate its magneto-thermopower behavior far beyond TC.

A possibility of holonomic quantum computation based on the defect-mediated properties of graphite cones is discussed. Using a geometric description for the conical graphene, we demonstrate how one can construct the most important one-qubit quantum gates without invoking the adiabatic approximation. The control parameter which defines a particular qubit configuration is directly linked with the number of removed sectors in the graphene layer needed to create a particular conical configuration.

A magnetic field induced electric polarization and the corresponding change of an effective junction capacitance are considered within a 3D model of disordered Josephson junction arrays. At some threshold field (near the Josephson network critical field), the effective junction charge and the related capacitance are shown to reach a maximum and to change a sign, respectively. A possibility to observe the predicted effects in artificially prepared arrays of superconducting grains is discussed.

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