On the boundary convergence of solutions to the Hermite-Schr\"odinger equation

In the half-space $\mathbb{R}^d \times \mathbb{R}_+$, we consider the Hermite-Schr\"odinger equation $i\partial u/\partial t = - \Delta u + |x|^2 u$, with given boundary values on $\mathbb{R}^d$. We prove a formula that links the solution of this problem to that of the classical Schr\"odinger equation. It shows that mixed norm estimates for the Hermite-Schr\"odinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary, by means of this link.Comment: 12 page

The Dynamics of Child Poverty in Sweden

The purpose of this paper is to study (empirically) the dynamics of child poverty in Sweden, the quintessential welfare state. We find that 1 out of every 5 children is disposable income poor at least once during his or her childhood, while only 2 percent of all children are chronically poor. We also document a strong life-cycle profile for child poverty. Just over 20 percent of all children are born into poverty. The average poverty rate then drops dramatically to about 7.5 percent among 1-year old children. After which, it declines (monotonically) to about 3.9 percent among 17-year olds. Children in Sweden are largely protected (economically) from a number of quite serious events, such as parental unemployment, sickness and death. Family dissolution and longterm unemployment, however, do push children into poverty. But for most of these children, poverty is only temporary. Single mothers, for example, are overrepresented among the poor, but not among the chronically poor. Children with immigrant parents are strongly overrepresented among the chronically poor; as are children whose parents have unusually low educations. We argue that information about the dynamics of child poverty may help policy makers to construct more salient policies for fighting child poverty.child poverty; chronic poverty; poverty dynamics

Derivation of the nonlinear fluctuating hydrodynamic equation from underdamped Langevin equation

We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in underdamped case. The steady state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.Comment: 16 page

Pressure induced structural and dynamical changes in liquid Si. An ab-initio study

The static and dynamic properties of liquid Si at high-pressure have been studied using the orbital free ab-initio molecular dynamics method. Four thermodynamic states at pressures 4, 8, 14 and 23 GPa are considered. The calculated static structure shows qualitative agreement with the available experimental data. We analize the remarkable structural changes occurring between 8 and 14 GPa along with its effect on several dynamic properties.Comment: 10 pages, 11 figures. Accepted for publication in Journal of Physics: Condensed Matte

Multiple-scattering effects on incoherent neutron scattering in glasses and viscous liquids

Incoherent neutron scattering experiments are simulated for simple dynamic models: a glass (with a smooth distribution of harmonic vibrations) and a viscous liquid (described by schematic mode-coupling equations). In most situations multiple scattering has little influence upon spectral distributions, but it completely distorts the wavenumber-dependent amplitudes. This explains an anomaly observed in recent experiments

Critical Decay at Higher-Order Glass-Transition Singularities

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted

Density fluctuations and single-particle dynamics in liquid lithium

The single-particle and collective dynamical properties of liquid lithium have been evaluated at several thermodynamic states near the triple point. This is performed within the framework of mode-coupling theory, using a self-consistent scheme which, starting from the known static structure of the liquid, allows the theoretical calculation of several dynamical properties. Special attention is devoted to several aspects of the single-particle dynamics, which are discussed as a function of the thermodynamic state. The results are compared with those of Molecular Dynamics simulations and other theoretical approaches.Comment: 31 pages (in preprint format), 14 figures. Submitted to Phys. Rev.

Feasibility of a self-help web-based intervention targeting young cancer patients with sexual problems and fertility distress

PURPOSE: The purpose of the study is to evaluate the feasibility of a self-help web-based intervention to alleviate sexual problems and fertility distress in adolescents and young adults with cancer. METHODS: Twenty-three persons with cancer (19 women and 4 men, age 18-43, 1-5 years post-diagnosis of lymphoma, breast, gynecologic, central nervous system, or testicular cancer) were recruited to test a 2-month web-based program targeting sexual problems or fertility distress. The programs were organized in modules with educational and behavior change content, including texts, illustrations, exercises, and video vignettes. The program also included a discussion forum and an "ask the expert" forum. In addition, the sexuality program offered two telephone consultations. Feasibility (regarding demand, acceptability, preliminary efficacy, and functionality) was evaluated with the website system data, telephone interviews, continuous online evaluations, and study-specific measures. RESULTS: Fifteen participants completed four modules or more. Most of the program features were used and well accepted by these "committed users." The web-based format enabled flexible use by participants with diverse needs. Preliminary efficacy was indicated by self-reported increased knowledge and skill in handling sexual problems and fertility distress. The website was easy to use and functioned well technically. CONCLUSIONS: The present study indicated that this web-based intervention was feasible for adolescents and young adults with cancer. The effectiveness of the intervention in decreasing sexual problems and fertility distress will be tested in a population-based randomized controlled trial for adolescents and young adults with cancer. TRIAL REGISTRATION: ISRCTN36621459

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.