Accurate quadratic-response approximation for the self-consistent pseudopotential of semiconductor nanostructures

Quadratic-response theory is shown to provide a conceptually simple but accurate approximation for the self-consistent one-electron potential of semiconductor nanostructures. Numerical examples are presented for GaAs/AlAs and InGaAs/InP (001) superlattices using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. When the reference crystal is chosen to be the virtual-crystal average of the two bulk constituents, the absolute error in the quadratic-response potential for Gamma(15) valence electrons is about 2 meV for GaAs/AlAs and 5 meV for InGaAs/InP. Low-order multipole expansions of the electron density and potential response are shown to be accurate throughout a small neighborhood of each reciprocal lattice vector, thus providing a further simplification that is confirmed to be valid for slowly varying envelope functions. Although the linear response is about an order of magnitude larger than the quadratic response, the quadratic terms are important both quantitatively (if an accuracy of better than a few tens of meV is desired) and qualitatively (due to their different symmetry and long-range dipole effects).Comment: 16 pages, 20 figures; v2: new section on limitations of theor

Finite-volume matrix elements of two-body states

In this talk, we present a framework for studying structural information of resonances and bound states coupling to two-hadron scattering states. This makes use of a recently proposed finite-volume formalism to determine a class of observables that are experimentally inaccessible but can be accessed via lattice QCD. In particular, we shown that finite-volume two-body matrix elements with one current insertion can be directly related to scattering amplitudes coupling to the external current. For two-hadron systems with resonances or bound states, one can extract the corresponding form factors of these from the energy-dependence of the amplitudes.Comment: 7 pages, 2 figures, Proceedings of Lattice 201

Uncertainty in the determination of soil hydraulic parameters and its influence on the performance of two hydrological models of different complexity

Data of soil hydraulic properties forms often a limiting factor in unsaturated zone modelling, especially at the larger scales. Investigations for the hydraulic characterization of soils are time-consuming and costly, and the accuracy of the results obtained by the different methodologies is still debated. However, we may wonder how the uncertainty in soil hydraulic parameters relates to the uncertainty of the selected modelling approach. We performed an intensive monitoring study during the cropping season of a 10 ha maize field in Northern Italy. The data were used to: i) compare different methods for determining soil hydraulic parameters and ii) evaluate the effect of the uncertainty in these parameters on different variables (i.e. evapotranspiration, average water content in the root zone, flux at the bottom boundary of the root zone) simulated by two hydrological models of different complexity: SWAP, a widely used model of soil moisture dynamics in unsaturated soils based on Richards equation, and ALHyMUS, a conceptual model of the same dynamics based on a reservoir cascade scheme. We employed five direct and indirect methods to determine soil hydraulic parameters for each horizon of the experimental profile. Two methods were based on a parameter optimization of: a) laboratory measured retention and hydraulic conductivity data and b) field measured retention and hydraulic conductivity data. The remaining three methods were based on the application of widely used Pedo-Transfer Functions: c) Rawls and Brakensiek, d) HYPRES, and e) ROSETTA. Simulations were performed using meteorological, irrigation and crop data measured at the experimental site during the period June – October 2006. Results showed a wide range of soil hydraulic parameter values generated with the different methods, especially for the saturated hydraulic conductivity Ksat and the shape parameter a of the van Genuchten curve. This is reflected in a variability of the modeling results which is, as expected, different for each model and each variable analysed. The variability of the simulated water content in the root zone and of the bottom flux for different soil hydraulic parameter sets is found to be often larger than the difference between modeling results of the two models using the same soil hydraulic parameter set. Also we found that a good agreement in simulated soil moisture patterns may occur even if evapotranspiration and percolation fluxes are significantly different. Therefore multiple output variables should be considered to test the performances of methods and model

Elimination of unoccupied state summations in it ab initio self-energy calculations for large supercells

We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set of reference energies. This improves the scaling of the computational time from the fourth to the third power of the number of atoms for both the inverse dielectric matrix and the self-energy, yielding improved efficiency for 8 or more silicon atoms per unit cell

Electron-phonon interaction in the solid form of the smallest fullerene C20_{20}

The electron-phonon coupling of a theoretically devised carbon phase made by assembling the smallest fullerenes C$_{20}$ is calculated from first principles. The structure consists of C$_{20}$ cages in an {\it fcc} lattice interlinked by two bridging carbon atoms in the interstitial tetrahedral sites ({\it fcc}-C$_{22}$). The crystal is insulating but can be made metallic by doping with interstitial alkali atoms. In the compound NaC$_{22}$ the calculated coupling constant $\lambda/N(0)$ is 0.28 eV, a value much larger than in C$_{60}$, as expected from the larger curvature of C$_{20}$. On the basis of the McMillan's formula, the calculated $\lambda$=1.12 and a $\mu^*$ assumed in the range 0.3-0.1 a superconducting T$_c$ in the range 15-55 K is predicted.Comment: 7 page

Relation Between EEG Measures and Upper Limb Motor Recovery in Stroke Patients: A Scoping Review

Current clinical practice does not leverage electroencephalography (EEG) measurements in stroke patients, despite its potential to contribute to post-stroke recovery predictions. We review the literature on the effectiveness of various quantitative and qualitative EEG-based measures after stroke as a tool to predict upper limb motor outcome, in relation to stroke timeframe and applied experimental tasks. Moreover, we aim to provide guidance on the use of EEG in the assessment of upper limb motor recovery after stroke, suggesting a high potential for some metrics in the appropriate context. We identified relevant papers (N = 16) from databases ScienceDirect, Web of Science and MEDLINE, and assessed their methodological quality with the Joanna Briggs Institute (JBI) Critical Appraisal. We applied the Preferred Reporting Systems for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews (PRISMA-ScR) Framework. Identified works used EEG to identify properties including event-related activation, spectral power in physiologically relevant bands, symmetry in brain dynamics, functional connectivity, cortico-muscular coherence and rhythmic coordination. EEG was acquired in resting state or in relation to behavioural conditions. Motor outcome was mainly evaluated with the Upper Limb Fugl-Meyer Assessment. Despite great variability in the literature, data suggests that the most promising EEG quantifiers for predicting post-stroke motor outcome are event-related measures. Measures of spectral power in physiologically relevant bands and measures of brain symmetry also show promise. We suggest that EEG measures may improve our understanding of stroke brain dynamics during recovery, and contribute to establishing a functional prognosis and choosing the rehabilitation approach

Integral quantification of seasonal soil moisture changes in farmland by cosmic-ray neutrons

Soil moisture at the plot or hill-slope scale is an important link between local vadose zone hydrology and catchment hydrology. However, so far only a few methods are on the way to close this gap between point measurements and remote sensing. One new measurement methodology that could determine integral soil moisture at this scale is the aboveground sensing of cosmic-ray neutrons, more precisely of ground albedo neutrons. The present study performed ground albedo neutron sensing (GANS) at an agricultural field in northern Germany. To test the method it was accompanied by other soil moisture measurements for a summer period with corn crops growing on the field and a later autumn-winter period without crops and a longer period of snow cover. Additionally, meteorological data and aboveground crop biomass were included in the evaluation. Hourly values of ground albedo neutron sensing showed a high statistical variability. Six-hourly values corresponded well with classical soil moisture measurements, after calibration based on one reference dry period and three wet periods of a few days each. Crop biomass seemed to influence the measurements only to minor degree, opposed to snow cover which has a more substantial impact on the measurements. The latter could be quantitatively related to a newly introduced field neutron ratio estimated from neutron counting rates of two energy ranges. Overall, our study outlines a procedure to apply the ground albedo neutron sensing method based on devices now commercially available, without the need for accompanying numerical simulations and suited for longer monitoring periods after initial calibration

Quadratic response theory for spin-orbit coupling in semiconductor heterostructures

This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A nonlinear response theory is developed for nonlocal spin-dependent perturbing potentials. The ionic pseudopotential of the heterostructure is treated as a perturbation of a bulk reference crystal, and the self-energy is derived to second order in the perturbation. If spin-orbit coupling is neglected outside the atomic cores, the problem can be analyzed as if the perturbation were a local spin scalar, since the nonlocal spin-dependent part of the pseudopotential merely renormalizes the results obtained from a local perturbation. The spin-dependent terms in the self-energy therefore fall into two classes: short-range potentials that are analytic in momentum space, and long-range nonanalytic terms that arise from the screened Coulomb potential multiplied by a spin-dependent vertex function. For an insulator at zero temperature, it is shown that the electronic charge induced by a given perturbation is exactly linearly proportional to the charge of the perturbing potential. These results are used in a subsequent paper to develop a first-principles effective-mass theory with generalized Rashba spin-orbit coupling.Comment: 20 pages, no figures, RevTeX4; v2: final published versio

Effect of inter-well interactions on non-linear beam splitters for matter-wave interferometers

We study the non-linear beam splitter in matter-wave interferometers using ultracold quantum gases in a double-well configuration in presence of non-local interactions inducing inter-well density-density coupling, as they can be realized, e.g., with dipolar gases. We explore this effect after considering different input states, in the form of either coherent, or Twin-Fock, or NOON states. We first review the non-interacting limit and the case in which only the local interaction is present, including the study of sensitivity near the self-trapping threshold. Then, we consider the two-mode model in the presence of inter-well interactions and consider the scaling of the sensitivity as a function of the non-local coupling strength. Our analysis clearly shows that non-local interactions can compensate the degradation of the sensitivity induced by local interactions, so that they may be used to restore optimal sensitivity