Anti-adiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas

We express the high-frequency (anti-adiabatic) limit of the exchange-correlation kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the kinetic stress tensor, the pair-correlation function, and the ground-state exchange-correlation potential. Of these quantities, the first three are amenable to exact evaluation by Quantum Monte Carlo methods, while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The anti-adiabatic xc kernels should be useful in calculations of excitation energies by time-dependent DFT in atoms, molecules, and solids, and provides a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.Comment: 9 pages, 3 figures, to be submitted to PR

Exchange and correlation energies of ground states of atoms and molecules in strong magnetic fields

Using a Hartree-Fock mesh method and a configuration interaction approach based on a generalized Gaussian basis set we investigate the behaviour of the exchange and correlation energies of small atoms and molecules, namely th e helium and lithium atom as well as the hydrogen molecule, in the presence of a magnetic field covering the regime B=0-100a.u. In general the importance of the exchange energy to the binding properties of at oms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions and in particular due to the contributions of the tightly bound hydrogenic state s which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.Comment: 4 Figures acc.f.publ.in Phys.Rev.

Nonlocal density functionals and the linear response of the homogeneous electron gas

The known and usable truly nonlocal functionals for exchange-correlation energy of the inhomogeneous electron gas are the ADA (average density approximation) and the WDA (weighted density approximation). ADA, by design, yields the correct linear response function of the uniform electron gas. WDA is constructed so that it is exact in the limit of one-electron systems. We derive an expression for the linear response of the uniform gas in the WDA, and calculate it for several flavors of WDA. We then compare the results with the Monte-Carlo data on the exchange-correlation local field correction, and identify the weak points of conventional WDA in the homogeneous limit. We suggest how the WDA can be modified to improve the response function. The resulting approximation is a good one in both opposite limits, and should be useful for practical nonlocal density functional calculations.Comment: 4 pages, two eps figures embedde

Positron and positronium affinities in the work-formalism Hartree-Fock approximation

Positron binding to anions is investigated within the work formalism proposed by Harbola and Sahni for the halide anions and the systems Li^- through O^- excluding Be^- and N^-. The toal ground-state energies of the anion-positron bound systems are empirically found to be an upper bound to the Hartree-Fock energies. The computed expectation values as well as positron and positronium affinities are in good agreement with their restricted Hartree-Fock counterparts. Binding of a positron to neutral species is also investigated using an iterative method.Comment: 12 pages, to appear in Physical Review

Impact of the COVID-19 pandemic on children with and without affective dysregulation and their families

Analyzing COVID-19-related stress in children with affective dysregulation (AD) seems especially interesting, as these children typically show heightened reactivity to potential stressors and an increased use of maladaptive emotion regulation strategies. Children in out-of-home care often show similar characteristics to those with AD. Since COVID-19 has led to interruptions in psychotherapy for children with mental health problems and to potentially reduced resources to implement treatment strategies in daily life in families or in out-of-home care, these children might show a particularly strong increase in stress levels. In this study, 512 families of children without AD and 269 families of children with AD reported on COVID-19-related stress. The sample comprised screened community, clinical, and out-of-home care samples. Sociodemographic factors, characteristics of child and caregiver before the pandemic, and perceived change in external conditions due to the pandemic were examined as potential risk or protective factors. Interestingly, only small differences emerged between families of children with and without AD or between subsamples: families of children with AD and families in out-of-home care were affected slightly more, but in few domains. Improvements and deteriorations in treatment-related effects balanced each other out. Overall, the most stable and strongest risk factor for COVID-19-related stress was perceived negative change in external conditions—particularly family conditions and leisure options. Additionally, caregiver characteristics emerged as risk factors across most models. Actions to support families during the pandemic should, therefore, facilitate external conditions and focus on caregiver characteristic to reduce familial COVID-19-related stress. Trial registration: German Clinical Trials Register (DRKS), ADOPT Online: DRKS00014963 registered 27 June 2018, ADOPT Treatment: DRKS00013317 registered 27 September 2018, ADOPT Institution: DRKS00014581 registered 04 July 2018

Dynamic correlations of the Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.Comment: 11 pages, 3 figures, submitted to PR

Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation

We use our recently developed functional bosonization approach to bosonize interacting fermions in arbitrary dimension $d$ beyond the Gaussian approximation. Even in $d=1$ the finite curvature of the energy dispersion at the Fermi surface gives rise to interactions between the bosons. In higher dimensions scattering processes describing momentum transfer between different patches on the Fermi surface (around-the-corner processes) are an additional source for corrections to the Gaussian approximation. We derive an explicit expression for the leading correction to the bosonized Hamiltonian and the irreducible self-energy of the bosonic propagator that takes the finite curvature as well as around-the-corner processes into account. In the special case that around-the-corner scattering is negligible, we show that the self-energy correction to the Gaussian propagator is negligible if the dimensionless quantities $( \frac{q_{c} }{ k_{F}} )^d F_{0} [ 1 + F_{0} ]^{-1} \frac{\mu}{\nu^{\alpha}} | \frac{ \partial \nu^{\alpha} }{ \partial \mu} |$ are small compared with unity for all patches $\alpha$. Here $q_{c}$ is the cutoff of the interaction in wave-vector space, $k_{F}$ is the Fermi wave-vector, $\mu$ is the chemical potential, $F_{0}$ is the usual dimensionless Landau interaction-parameter, and $\nu^{\alpha}$ is the {\it{local}} density of states associated with patch $\alpha$. We also show that the well known cancellation between vertex- and self-energy corrections in one-dimensional systems, which is responsible for the fact that the random-phase approximation for the density-density correlation function is exact in $d=1$, exists also in $d> 1$, provided (1) the interaction cutoff $q_{c}$ is small compared with $k_{F}$, and (2) the energy dispersion is locally linearized at the Fermi the Fermi surface. Finally, we suggest a new systematic method to calculate corrections to the RPA, which is based on the perturbative calculation of the irreducible bosonic self-energy arising from the non-Gaussian terms of the bosonized Hamiltonian.Comment: The abstract has been rewritten. No major changes in the text

Cognitive decline in Huntington's disease expansion gene carriers

BACKGROUND: In Huntington's Disease (HD) cognitive decline can occur before unequivocal motor signs become apparent. As cognitive decline often starts early in the course of the disease and has a progressive nature over time, cognition can be regarded as a key target for symptomatic treatment. The specific progressive profile of cognitive decline over time is unknown. OBJECTIVE: The aim of this study is to quantify the progression of cognitive decline across all HD stages, from pre-motormanifest to advanced HD, and to investigate if CAG length mediates cognitive decline. METHODS: In the European REGISTRY study 2669 HD expansion gene carriers underwent annual cognitive assessment. General linear mixed models were used to model the cognitive decline for each cognitive task across all disease stages. Additionally, a model was developed to evaluate the cognitive decline based on CAG length and age rather than disease stage. RESULTS: There was significant cognitive decline on all administered tasks throughout pre-motormanifest (close to estimated disease onset) participants and the subsequent motormanifest participants from stage 1 to stage 4. Performance on the Stroop Word and Stroop Color tests additionally declined significantly across the two pre-motormanifest groups: far and close to estimated disease onset. The evaluation of cognition performance in relation to CAG length and age revealed a more rapid cognitive decline in participants with longer CAG length than participants with shorter CAG length over time. CONCLUSION: Cognitive performance already shows decline in pre-motormanifest HD gene expansion carriers and gradually worsens to late stage HD. HD gene expansion carriers with certain CAG length have their own cognitive profile, i.e., longer CAG length is associated with more rapid decline