Convergence to Scattering States in the Nonlinear Schr\"odinger Equation

In this paper, we consider global solutions of the following nonlinear Schr\"odinger equation $iu_t+\Delta u+\lambda|u|^\alpha u = 0,$ in $\R^N,$ with $\lambda\in\R,$ $\alpha\in(0,\frac{4}{N-2})$ $(\alpha\in(0,\infty)$ if $N=1)$ and \linebreak $u(0)\in X\equiv H^1(\R^N)\cap L^2(|x|^2;dx).$ We show that, under suitable conditions, if the solution $u$ satisfies $e^{-it\Delta}u(t)-u_ \pm\to0$ in $X$ as $t\to\pm\infty$ then $u(t)-e^{it\Delta}u_\pm\to0$ in $X$ as $t\to\pm\infty.$ We also study the converse. Finally, we estimate $|\:\|u(t)\|_X-\|e^{it\Delta}u_\pm\|_X\:|$ under some less restrictive assumptions

Laser anneal of oxycarbosilane low-k film

Submilisecond laser anneal has been experimentally investigated for porogen removal and its ability to improve the mechanical strength in oxycarbosilane ultra low-k films compromised due to the introduction of porosity. We report the occurrence of extensive bond rearrangements inferred from Fourier-transform infra-red (FTIR) spectroscopy, elastic recoil detection (ERD) and spectroscopic ellipsometry (SE) in the energy range of 1.4-8 eV. The laser anneal affects most notably the organic content of the organosilicate matrix leading to depletion and reorganization. Nevertheless, the tested conditions reveal a processing window which allows for 13% improvement of Young’s modulus as compared to the reference film, annealed in a conventional furnace at 400°C for 2 h, while not impacting the relative dielectric constant of 2.25

Critical behavior of the 3-state Potts model on Sierpinski carpet

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations, for a Hausdorff dimension $d_{f}$ $\simeq 1.8928$. The phase transition is shown to be a second order one. The maxima of the susceptibility of the order parameter follow a power law in a very reliable way, which enables us to calculate the ratio of the exponents $\gamma /\nu$. We find that the scaling corrections affect the behavior of most of the thermodynamical quantities. However, the sequence of intersection points extracted from the Binder's cumulant provides bounds for the critical temperature. We are able to give the bounds for the exponent $1/\nu$ as well as for the ratio of the exponents $\beta/\nu$, which are compatible with the results calculated from the hyperscaling relation.Comment: 13 pages, 4 figure

Embedded Systems Requirements Verification Using HiLeS Designer

International audienceOne of the issues related to systems design is the early verification in first design steps: system specifications verification. Nowadays, it is common to use text-based specifications to begin a system design. However, these specifications cannot be verified until a software model is made. In this work, we show how can we use HiLeS Designer to model and verify, formally and by simulation an embedded system specification. This tool makes easier to build the model, using graphical concepts which are familiar to designers. It also helps to verify formally the structure and some logical behavior, and by simulation, it is possible to verify the consistence of the embedded system specification. We model and verify System Display Selector Requirements applying HiLeS Designer

Investing Retirement Wealth: A Life-Cycle Model

If household portfolios are constrained by borrowing and short-sales restrictions asset markets, then alternative retirement savings systems may affect household welfare by relaxing these constraints. This paper uses a calibrated partial-equilibrium model of optimal life-cycle portfolio choice to explore the empirical relevance of these issues. In a benchmark case, we find ex-ante welfare gains equivalent to a 3.7% increase in consumption from the investment of half of retirement wealth in the equity market. The main channel through which these gains are realized is that the higher average return on equities permits a lower Social Security tax rate on younger households, which helps households smooth their consumption over the life cycle. There is a smaller welfare gain of 0.5% of consumption when Social Security tax rates are held constant. We also find that realistic heterogeneity of risk aversion and labor income risk can strongly affect optimal portfolio choice over the life cycle, which provides one argument for a privatized Social Security system with an element of personal portfolio choice.

Stock Market Mean Reversion and the Optimal Equity Allocation of a Long-Lived Investor

This paper solves numerically the intertemporal consumption and portfolio choice problem of an infinitely-lived investor who faces a time-varying equity premium. The solutions we obtain are very similar to the approximate analytical solutions of Campbell and Viceira (1999), except at the upper extreme of the state space where both the numerical consumption and portfolio rules flatten out. We also consider a constrained version of the problem in which the investor faces borrowing and short-sales restrictions. These constraints bind when the equity premium moves away from its mean in either direction, and are particularly severe for risk-tolerant investors. The constraints have substantial effects on optimal consumption, but much more modest effects on optimal portfolio choice in the region of the state space where they are not binding.Economic

Coupling between electronic and structural degrees of freedom in the triangular lattice conductor NaxCoO2

The determination by powder neutron diffraction of the ambient temperature crystal structures of compounds in the NaxCoO2 family, for 0.3 < x <= 1.0, is reported. The structures consist of triangular CoO2 layers with Na ions distributed in intervening charge reservoir layers. The shapes of the CoO6 octahedra that make up the CoO2 layers are found to be critically dependent on the electron count and on the distribution of the Na ions in the intervening layers, where two types of Na sites are available. Correlation of the shapes of cobalt-oxygen octahedra, the Na ion positions, and the electronic phase diagram in NaxCoO2 is made, showing how structural and electronic degrees of freedom can be coupled in electrically conducting triangular lattice systems.Comment: 15 pages, 1 tables, 6 figures Submitted to Physical Review

Joule-assisted silicidation for short-channel silicon nanowire devices

We report on a technique enabling electrical control of the contact silicidation process in silicon nanowire devices. Undoped silicon nanowires were contacted by pairs of nickel electrodes and each contact was selectively silicided by means of the Joule effect. By a realtime monitoring of the nanowire electrical resistance during the contact silicidation process we were able to fabricate nickel-silicide/silicon/nickel- silicide devices with controlled silicon channel length down to 8 nm.Comment: 6 pages, 4 figure

Atom chip based generation of entanglement for quantum metrology

Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing, and quantum metrology. Here we report experiments where we generate multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We employ this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are useful for quantum metrology. The observed 3.7 dB reduction in spin noise combined with the spin coherence imply four-partite entanglement between the condensate atoms and could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques demonstrated here could be directly applied in chip-based atomic clocks which are currently being set up