David Hochstuhl

Two-photon ionization of helium studied with the multiconfigurational time-dependent Hartree–Fock method

The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is applied for simulations of the two-photon ionization of helium. We present results for the single and double ionizations from the ground state for photon energies in the nonsequential regime and compare them to direct solutions of the Schrödinger equation using the time-dependent (full) configuration interaction (TDCI) method. We find that the single ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI.

Application of neural networks with back-propagation to genome-enabled prediction of complex traits in Holstein-Friesian and German Fleckvieh cattle

BackgroundRecently, artificial neural networks (ANN) have been proposed as promising machines for marker-based genomic predictions of complex traits in animal and plant breeding. ANN are universal approximators of complex functions, that can capture cryptic relationships between SNPs (single nucleotide polymorphisms) and phenotypic values without the need of explicitly defining a genetic model. This concept is attractive for high-dimensional and noisy data, especially when the genetic architecture of the trait is unknown. However, the properties of ANN for the prediction of future outcomes of genomic selection using real data are not well characterized and, due to high computational costs, using whole-genome marker sets is difficult. We examined different non-linear network architectures, as well as several genomic covariate structures as network inputs in order to assess their ability to predict milk traits in three dairy cattle data sets using large-scale SNP data. For training, a regularized back propagation algorithm was used. The average correlation between the observed and predicted phenotypes in a 20 times 5-fold cross-validation was used to assess predictive ability. A linear network model served as benchmark.ResultsPredictive abilities of different ANN models varied markedly, whereas differences between data sets were small. Dimension reduction methods enhanced prediction performance in all data sets, while at the same time computational cost decreased. For the Holstein-Friesian bull data set, an ANN with 10 neurons in the hidden layer achieved a predictive correlation of r=0.47 for milk yield when the entire marker matrix was used. Predictive ability increased when the genomic relationship matrix (r=0.64) was used as input and was best (r=0.67) when principal component scores of the marker genotypes were used. Similar results were found for the other traits in all data sets.ConclusionArtificial neural networks are powerful machines for non-linear genome-enabled predictions in animal breeding. However, to produce stable and high-quality outputs, variable selection methods are highly recommended, when the number of markers vastly exceeds sample size.

Photoelectron circular dichroism in the multiphoton ionization by short laser pulses. I. Propagation of single-active-electron wave packets in chiral pseudo-potentials.

A theoretical method to study the angle-resolved multiphoton ionization of polyatomic molecules is developed. It is based on the time-dependent formulation of the Single Center (TDSC) method and consists in the propagation of single-active-electron wave packets in the effective molecular potentials in the presence of intense laser pulses. For this purpose, the time-dependent Schrödinger equation for one electron, moving in a molecular field and interacting with an arbitrary laser pulse, is solved in spherical coordinates by an efficient numerical approach. As a test, the method is applied to the one- and two-photon ionizations of a model methane-like chiral system by circularly polarized short intense high-frequency laser pulses. Thereby, we analyze the photoelectron circular dichroism (PECD) in the momentum distribution. The considered model application illustrates the capability of the TDSC method to study multiphoton PECD in fixed-in-space and randomly oriented chiral molecules.

Multiconfigurational time-dependent Hartree-Fock calculations for photoionization of one-dimensional Helium

The multiconfigurational time-dependent Hartree-Fock equations are discussed and solved for a one-dimensional model of the Helium atom. Results for the ground state energy and two-particle density as well as the absorption spectrum are presented and compared to direct solutions of the time-dependent Schrodinger equation.

Time-dependent restricted active space Configuration Interaction theory applied to the photoionization of neon

We give a presentation on the time-dependent restricted active space Configuration Interaction method, which has been recently introduced [D. Hochstuhl, M. Bonitz, PRA, in press] to efficiently tackle the few-particle nonequilibrium many-body problem. Particularly, we apply it to the calculation of photoionization cross sections and angular resolved ionization yields of groundstate neon.

Nonequilibrium Green function approach to photoionization processes in atoms

Abstract We present a quantum kinetic approach for the time-resolved description of many-effects in photoionization processes in atoms. The method is based on the non-equilibrium Green functions formalism and solves the Keldysh/Kadanoff–Baym equations in second Born approximation. An approximation scheme is introduced and discussed, which provides a complete single-particle description of the continuum, while the atom is treated fully correlated.

Quantum breathing mode of interacting particles in harmonic traps

The breathing mode – the uniform radial expansion and contraction of a system of interacting particles – is analyzed. Extending our previous work [Bauch et al 2009 Phys. Rev. B. 80 054515] we present a systematic analysis of the breathing mode for fermions with an inverse power law interaction potential w(r) ~ r−dwith d = 1,2,3 in the whole range of coupling parameters. The results thus cover the range from the ideal gas to the Wigner crystal-like state. In addition to exact results for two particles obtained from a solution of the time-dependent Schrodinger equation we present results for N = 4,6 from multiconfiguration time-dependent Hartree-Fock simulations.