Investigations of noise and of quantum interference in proximity effect bridges

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2.

If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation.

The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text.

The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices.

We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by <V^2(f ) > = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.

Proximity effect in Ag-Pb alloys

The superconducting properties and the microstructure of the Ag_100-xPb_x alloys, 1 ≤ x ≤ 5, prepared by rapid quenching from the liquid state with and without subsequent heat treatments, have been studied. The x-ray diffraction measurements show that supersaturated solid solutions of Pb in Ag can be obtained up to 3.2 at.% Pb as compared to less than 0.1 at.% Pb at equilibrium. It was found that by suitable heat treatment it is possible to vary the size and distribution of the Pb precipitates in the Ag matrix and reproducible superconducting properties in the alloy can be observed. The superconducting transition temperature of these samples can be qualitatively explained by the Silvert and Singh's theoretical calculation. The theory developed for the case of layer structure can be extended to three dimensions to explain the critical current versus temperature behavior. The critical current versus field behavior of these alloys can be explained by the modification of the Josephson effect. Combining these results together with the critical magnetic field measurements and the microstructure studies of the alloys, it can be concluded that the three-dimensional proximity effect is the main mechanism for the superconductivity in the Ag-Pb alloys. Based on the Hilsch empirical formula which was based on experimental results obtained on layer structures, the experimental data in this investigation show that the electron-phonon-electron interaction in silver is attractive. The interaction parameter NV obtained is approximately 0.06, which would lead to a value of 10^-5 °K for the superconducting transition temperature of Ag. These values are in agreement with other determinations which were done on vapor-deposited metallic film sandwiches. Hence, the Hilsch empirical relation valid for layer structures is also valid in the three-dimensional case. Because the transition temperature and the critical current can be varied in a wide range by controlling the heat treatments, the Ag-Pb superconductors might have some useful applications.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Double proximity effect in lateral S-NF-S junctions

We investigate planar Josephson junctions where the intermediate spacer between the two superconductors is an hybrid structure made by a normal metal and a ferromagnet. The different behaviors of the S-N-S junctions with thicknesses of 50 nm in both Cu and Nb layers, and S-N/F-S junctions with 10 nm of Co, 50 nm of Cu and 50 nm of Nb are studied. In this way, we analyze the influence of the ferromagnetic exchange interaction on the proximity effect. A dramatic supression of the josephson critical current of the Nb-(Cu/Co)-Nb junctions is observed. We believe that the reason for this is due to the length scale of the superconducting correlations of the electrons and holes of the weak link is larger than the thickness of Cu/Co bilayer.

Monitoring tunnel deformation induced by close-proximity bored tunneling using distributed optical fiber strain measurements

The paper describes the use of optical fiber Brillouin Optical Time Domain Reflectometry (BOTDR) to monitor the strain distribution in an existing tunnel while a twin tunnel was bored at close-proximity. The twin circular bored tunnels between Serangoon and Bartley stations on the new Circle Line Stage 3 subway in Singapore were constructed at close-proximity to avoid underpinning the foundations of adjacent buildings. The minimum clear separation of the two tunnels is 2.3m (0.4 times the tunnel diameter). The Outer Tunnel was constructed first, followed by the Inner Tunnel, with the earth-pressure balance tunnel boring machines maintained at a minimum of 100m apart. In this trial application of BOTDR, the strain distribution along the Outer Tunnel was measured, in order to monitor its deformation due to the boring of the Inner Tunnel at close-proximity. The aim of the trial application was to determine the practicality of this monitoring method for future use in 'live' tunnels. This paper compares the measurements obtained from optical fiber BOTDR with conventional methods of tunnel monitoring and describes preliminary installation and workmanship guidelines derived from lessons learnt during this trial. © 2007 ASCE.

Monte Carlo-Based Bayesian group object tracking and causal reasoning

We present algorithms for tracking and reasoning of local traits in the subsystem level based on the observed emergent behavior of multiple coordinated groups in potentially cluttered environments. Our proposed Bayesian inference schemes, which are primarily based on (Markov chain) Monte Carlo sequential methods, include: 1) an evolving network-based multiple object tracking algorithm that is capable of categorizing objects into groups, 2) a multiple cluster tracking algorithm for dealing with prohibitively large number of objects, and 3) a causality inference framework for identifying dominant agents based exclusively on their observed trajectories.We use these as building blocks for developing a unified tracking and behavioral reasoning paradigm. Both synthetic and realistic examples are provided for demonstrating the derived concepts. © 2013 Springer-Verlag Berlin Heidelberg.

Negative Effects of Relative Proximity and Absolute Geography on Open Innovation Practices in High-tech SMEs in the UK

© 2014 IEEE. This exploratory study addresses a gap in management literature by addressing the role of location in the continuously expanding field of open innovation research. In this context, we analyze potential negative effects of absolute geography and relative proximity on open innovation practices in high-tech small and medium-sized enterprises (SMEs) in the United Kingdom. Drawing upon cluster theory and business ecosystem literature, the analysis from three SME case studies in the East of England suggests that presumed 'favorable' location variables, such as close relative proximity between partners and the presence of economic clusters, can have certain negative effects on open innovation practices.

Loschmidt echo and Berry phase of a quantum system coupled to an XY spin chain: Proximity to a quantum phase transition

We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter lambda in spin chain diverges along the critical line lambda=1, which suggests an alternative measurement of the quantum criticality of the spin chain.

Spectral properties of a double-quantum-dot structure: A causal Green's function approach

Spectral properties of a double quantum dot (QD) structure are studied by a causal Green's function (GF) approach. The double QD system is modeled by an Anderson-type Hamiltonian in which both the intra- and interdot Coulomb interactions are taken into account. The GF's are derived by an equation-of-motion method and the real-space renormalization-group technique. The numerical results show that the average occupation number of electrons in the QD exhibits staircase features and the local density of states depends appreciably on the electron occupation of the dot.

Motivated Action Theory: A Formal Theory of Causal Reasoning

When we reason about change over time, causation provides an implicit preference: we prefer sequences of situations in which one situation leads causally to the next, rather than sequences in which one situation follows another at random and without causal connections. In this paper, we explore the problem of temporal reasoning --- reasoning about change over time --- and the crucial role that causation plays in our intuitions. We examine previous approaches to temporal reasoning, and their shortcomings, in light of this analysis. We propose a new system for causal reasoning, motivated action theory, which builds upon causation as a crucial preference creterion. Motivated action theory solves the traditional problems of both forward and backward reasoning, and additionally provides a basis for a new theory of explanation.