Spreading and shortest paths in systems with sparse long-range connections

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered by the spreading quantity on an infinite system is exactly calculated in all dimensions. We find that V(t) grows initially as t^d/d for t>t^*$, generalizing a previous result in one dimension. Using the properties of V(t), the average shortest-path distance \ell(r) can be calculated as a function of Euclidean distance r. It is found that \ell(r) = r for r<r_c=(2p \Gamma_d (d-1)!)^{-1/d} log(2p \Gamma_d L^d), and \ell(r) = r_c for r>r_c. The characteristic length r_c, which governs the behavior of shortest-path lengths, diverges with system size for all p>0. Therefore the mean separation s \sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for shortest-path lengths. We notice however that the globally averaged shortest-path length, divided by L, is a function of L/s only.Comment: 4 pages, 1 eps fig. Uses psfi

Spin Dependence of Interfacial Reflection Phase Shift at Cu/Co Interface

The spin dependent reflection at the interface is the key element to understand the spin transport. By completely solving the scattering problem based on first principles method, we obtained the spin resolved reflectivity spectra. The comparison of our theoretical results with experiment is good in a large energy scale from Fermi level to energy above vacuum level. It is found that interfacial distortion is crucial for understanding the spin dependence of the phase gain at the Cu$|$Co interface. Near the Fermi level, image state plays an important role to the phase accumulation in the copper film.Comment: 6 papges, 3 figures, accepted by Physical Review

Spin-polarized tunneling spectroscopy in tunnel junctions with half-metallic electrodes

We have studied the magnetoresistance (TMR) of tunnel junctions with electrodes of La2/3Sr1/3MnO3 and we show how the variation of the conductance and TMR with the bias voltage can be exploited to obtain a precise information on the spin and energy dependence of the density of states. Our analysis leads to a quantitative description of the band structure of La2/3Sr1/3MnO3 and allows the determination of the gap delta between the Fermi level and the bottom of the t2g minority spin band, in good agreement with data from spin-polarized inverse photoemission experiments. This shows the potential of magnetic tunnel junctions with half-metallic electrodes for spin-resolved spectroscopic studies.Comment: To appear in Physical Review Letter

Evolution of reference networks with aging

We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barab\'{a}si-Albert's model and (ii) to $\tau^{-\alpha}$, where $\tau$ is the age of the old site. We consider $\alpha$ of any sign although reasonable values are $0 \leq \alpha \leq \infty$. We find both from simulation and analytically that the network shows scaling behavior only in the region $\alpha < 1$. When $\alpha$ increases from $-\infty$ to 0, the exponent $\gamma$ of the distribution of connectivities ($P(k) \propto k^{-\gamma}$ for large $k$) grows from 2 to the value for the network without aging, i.e. to 3 for the Barab\'{a}si-Albert's model. The following increase of $\alpha$ to 1 makes $\gamma$ to grow to $\infty$. For $\alpha>1$ the distribution $P(k)$ is exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure

Ising model in small-world networks

The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the thermodynamic limit, the phase transition has a mean-field character for any finite value of the rewiring probability p, which measures the disorder strength of a given network. For small values of p, both the transition temperature and critical energy change with p as a power law. In the limit p -> 0, the heat capacity at the transition temperature diverges logarithmically in two-dimensional (2D) networks and as a power law in 3D.Comment: 6 pages, 7 figure

Spatiotemporal Characterization of Supercontinuum Extending from the Visible to the Mid-Infrared in Multimode Graded-Index Optical Fiber

We experimentally demonstrate that pumping a graded-index multimode fiber with sub-ns pulses from a microchip Nd:YAG laser leads to spectrally flat supercontinuum generation with a uniform bell-shaped spatial beam profile extending from the visible to the mid-infrared at 2500\,nm. We study the development of the supercontinuum along the multimode fiber by the cut-back method, which permits us to analyze the competition between the Kerr-induced geometric parametric instability and stimulated Raman scattering. We also performed a spectrally resolved temporal analysis of the supercontinuum emission.Comment: 5 pages 7 figure

Quantized conductance in a one-dimensional ballistic oxide nanodevice

Electric-field effect control of two-dimensional electron gases (2-DEG) has enabled the exploration of nanoscale electron quantum transport in semiconductors. Beyond these classical materials, transition metal-oxide-based structures have d-electronic states favoring the emergence of novel quantum orders absent in conventional semiconductors. In this context, the LaAlO3/SrTiO3 interface that combines gate-tunable superconductivity and sizeable spin-orbit coupling is emerging as a promising platform to realize topological superconductivity. However, the fabrication of nanodevices in which the electronic properties of this oxide interface can be controlled at the nanoscale by field-effect remains a scientific and technological challenge. Here, we demonstrate the quantization of conductance in a ballistic quantum point contact (QPC), formed by electrostatic confinement of the LaAlO3/SrTiO3 2-DEG with a split-gate. Through finite source-drain voltage, we perform a comprehensive spectroscopic investigation of the 3d energy levels inside the QPC, which can be regarded as a spectrometer able to probe Majorana states in an oxide 2-DEG

Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model

We generalize the Barab\'{a}si--Albert's model of growing networks accounting for initial properties of sites and find exactly the distribution of connectivities of the network $P(q)$ and the averaged connectivity $\bar{q}(s,t)$ of a site $s$ in the instant $t$ (one site is added per unit of time). At long times $P(q) \sim q^{-\gamma}$ at $q \to \infty$ and $\bar{q}(s,t) \sim (s/t)^{-\beta}$ at $s/t \to 0$, where the exponent $\gamma$ varies from 2 to $\infty$ depending on the initial attractiveness of sites. We show that the relation $\beta(\gamma-1)=1$ between the exponents is universal.Comment: 4 pages revtex (twocolumn, psfig), 1 figur