Nonlinear terahertz spectroscopy of semiconductor nanostructures

Nonlinear frequency conversion and electro-optic sampling allow for the generation and phase-resolved characterization of few-cycle pulses in the frequency range up to 50 THz. Electric field transients with amplitudes of up to several MV/cm are applied to study coherent nonlinear excitations of low-dimensional semiconductors. We report the first observation of Rabi oscillations on intersubband transitions of electrons in GaAs/AlGaAs quantum wells. Frequency and phase of such oscillations are controlled in the 0.3- to 2.5-THz range via the strength and shape of the mid-infrared driving pulse. PACS 78.67.De; 73.21.Fg; 07.57.Hm; 42.65.Re     

Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations

On the basis of spectral-expansion Green's function theory, we theoretically describe the topography, polarization, and spatial-coherence properties of the second-harmonic (SH) local fields at rough metal surfaces. The spatial distributions of the fundamental frequency and SH local fields are very different, with highly enhanced hot spots of the SH. The spatial correlation functions of the amplitude, phase, and direction of the SH polarization all show spatial decay on the nanoscale in the wide range of the metal fill factors. This implies that SH radiation collected from even nanometer-scale areas is strongly depolarized and dephased, i.e., has the nature of hyper-Rayleigh scattering, in agreement with recent experiments. The present theory is applicable to nanometer-scale nonlinear-optical illumination, probing, and modification.     

The extent to which subsets are additively closed

Given a finite abelian group G (written additively), and a subset S of G, the size r(S) of the set may range between 0 and ²|S|, with the extremal values of r(S) corresponding to sum-free subsets and subgroups of G. In this paper, we consider the intermediate values which r(S) may take, particularly in the setting where G is Z/pZ under addition (p prime). We obtain various bounds and results. In the Z/pZ setting, this work may be viewed as a subset generalization of the Cauchy-Davenport Theorem.     

Cluster TOF-SIMS imaging of human skin remains: analysis of a South-Andean mummy sample

A skin sample from a South-Andean mummy dating back from the XI(th) century was analyzed using time-of-flight secondary ion mass spectrometry imaging using cluster primary ion beams (cluster-TOF-SIMS). For the first time on a mummy, skin dermis and epidermis could be chemically differentiated using mass spectrometry imaging. Differences in amino-acid composition between keratin and collagen, the two major proteins of skin tissue, could indeed be exploited. A surprising lipid composition of hypodermis was also revealed and seems to result from fatty acids damage by bacteria. Using cluster-TOF-SIMS imaging skills, traces of bio-mineralization could be identified at the micrometer scale, especially formation of calcium phosphate at the skin surface. Mineral deposits at the surface were characterized using both scanning electron microscopy (SEM) in combination with energy-dispersive X-ray spectroscopy and mass spectrometry imaging. The stratigraphy of such a sample was revealed for the first time using this technique. More precise molecular maps were also recorded at higher spatial resolution, below 1?μm. This was achieved using a non-bunched mode of the primary ion source, while keeping intact the mass resolution thanks to a delayed extraction of the secondary ions. Details from biological structure as can be seen on SEM images are observable on chemical maps at this sub-micrometer scale. Thus, this work illustrates the interesting possibilities of chemical imaging by cluster-TOF-SIMS concerning ancient biological tissues.     

Micro/macro viability analysis of individual‐based models: Investigation into the viability of a stylized agricultural cooperative

The mathematical viability theory proposes methods and tools to study at a global level how controlled dynamical systems can be confined in a desirable subset of the state space. Multilevel viability problems are rarely studied since they induce combinatorial explosion (the set of N agents each evolving in a p‐dimensional state space, can evolve in a Np dimensional state space). In this article, we propose an original approach which consists in solving first local viability problems and then studying the real viability of the combination of the local strategies, by simulation where necessary. In this article, we consider as multilevel viability problem a stylized agricultural cooperative which has to keep a minimum of members. Members have an economical constraint and some members have a simple model of the functioning of the cooperative and make assumptions on other members' behavior, especially proviable agents which are concerned about their own viability. In this framework, the model assumptions allow us to solve the local viability problem at the agent level. At the cooperative level, considering mixture of agents, simulation results indicate if and when including proviable agents increases the viability of the whole cooperative. © 2014 Wiley Periodicals, Inc. Complexity 21: 276–296, 2015     

High quality and tuneable silica shell–magnetic core nanoparticles

Obtaining small (<50 nm), monodispersed, well-separated, single iron oxide core–silica (SiO₂) shell nanoparticles for biomedical applications is still a challenge. Preferably, they are synthesised by inverse microemulsion method. However, substantial amount of aggregated and multicore core–shell nanoparticles is the undesired outcome of the method. In this study, we report on the production of less than 50 nm overall size, monodispersed, free of necking, single core iron oxide–SiO₂ shell nanoparticles with tuneable shell thickness by a carefully optimized inverse microemulsion method. The high degree of control over the process is achieved by understanding the mechanism of core–shell nanoparticles formation. By varying the reaction time and precursor concentration, the thickness of silica layer on the core nanoparticles can be finely adjusted from 5 to 13 nm. Residual reactions during the workup were inhibited by a combination of pH control with shock freezing and ultracentrifuging. These high-quality tuneable core–shell nanocomposite particles exhibit superparamagnetic character and sufficiently high magnetization with great potential for biomedical applications (e.g. MRI, cell separation and magnetically driven drug delivery systems) either as-prepared or by additional surface modification for improved biocompatibility.     

Typicality of Pure States Randomly Sampled According to the Gaussian Adjusted Projected Measure

Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator ρ of low purity, tr ρ ² ≪1, and yielding the ensemble averaged expectation value tr (ρ A) for any observable A. Assuming that the given statistical ensemble ρ is generated by randomly sampling pure states |ψ〉 according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value 〈ψ|A|ψ〉 is shown to be extremely close to the ensemble average tr (ρ A) for the overwhelming majority of pure states |ψ〉 and any experimentally realistic observable A. In particular, such a ‘typicality’ property holds  whenever the Hilbert space ℋ of the system contains a high dimensional subspace ℋ₊⊂ℋ with the property that all |ψ〉∈ℋ₊ are realized with equal probability and all other |ψ〉∈ℋ are excluded.     

Functional semiparametric partially linear model with autoregressive errors

In this paper, we introduce a functional semiparametric model, where a real-valued random variable is explained by the sum of a unknown linear combination of the components of a multivariate random variable and an unknown transformation of a functional random variable. The errors can be autocorrelated. We focus here on the parametric estimation of the coefficients in the linear combination. First, we use a nonparametric kernel method to remove the effect of the functional explanatory variable. Then, we use generalized least squares approach to obtain an estimator of these coefficients. Under some technical assumptions, we prove consistency and asymptotic normality of our estimator. Finally, we present Monte Carlo simulations that illustrate these characteristics.