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 Schroedinger equation.Comment: 10 pages, 3 figures, 1 tabl

Effective Josephson dynamics in resonantly driven Bose-Einstein condensates

We show that the orbital Josephson effect appears in a wide range of driven atomic Bose-Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: Gross-Pitaevskii equation, exact diagonalization of the few-mode problem, and the Multi-Configurational Time-Dependent Hartree for Bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that they represent the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point, and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the (t,t')-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.Comment: 14 pages, 9 figure

Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models

In this contribution, we discuss the finite-element discrete variable representation (FE-DVR) of the nonequilibrium Green's function and its implications on the description of strongly inhomogeneous quantum systems. In detail, we show that the complementary features of FEs and the DVR allows for a notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations compared to a general basis approach. Particularly, the use of the FE-DVR leads to an essential speedup in computing the self-energies. As atomic and molecular examples we consider the He atom and the linear version of H$_3^+$ in one spatial dimension. For these closed-shell models we, in Hartree-Fock and second Born approximation, compute the ground-state properties and compare with the exact findings obtained from the solution of the few-particle time-dependent Schr\"odinger equation.Comment: 12 pages, 3 figures, submitted as proceedings of conference "PNGF IV

Introduction to Configuration Path Integral Monte Carlo

In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most successful approaches to first-principle simulations of many-body quantum systems. In this chapter we present a recently developed method---the configuration path integral Monte Carlo (CPIMC) method for moderately coupled, highly degenerate fermions at finite temperatures. It is based on the second quantization representation of the $N$-particle density operator in a basis of (anti-)symmetrized $N$-particle states (configurations of occupation numbers) and allows to tread arbitrary pair interactions in a continuous space. We give a detailed description of the method and discuss the application to electrons or, more generally, Coulomb-interacting fermions. As a test case we consider a few quantum particles in a one-dimensional harmonic trap. Depending on the coupling parameter (ratio of the interaction energy to kinetic energy), the method strongly reduces the sign problem as compared to direct path integral Monte Carlo (DPIMC) simulations in the regime of strong degeneracy which is of particular importance for dense matter in laser plasmas or compact stars. In order to provide a self-contained introduction, the chapter includes a short introduction to Metropolis Monte Carlo methods and the second quantization of quantum mechanics.Comment: chapter in book "Introduction to Complex Plasmas: Scientific Challenges and Technological Opportunities", Michael Bonitz, K. Becker, J. Lopez and H. Thomsen (Eds.) Springer Series "Atomic, Optical and Plasma Physics", vol. 82, Springer 2014, pp. 153-194 ISBN: 978-3-319-05436-0 (Print) 978-3-319-05437-7 (Online

Nonequilibrium Green function approach to photoionization processes in atoms

We present a quantum kinetic approach for the time-resolved description of many-body 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.Comment: 11 pages, 6 figure

Time-dependent multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms

Numerical simulations present an indispensable way to the understanding of complex physical processes. In quantum mechanics where the theoretical description is given in terms of the time-dependent Schrödinger equation the road is, however, difficult for any but the simplest systems. This is particularly true if one considers photoionization processes of atoms and molecules which, at the same time, require an accurate description of bound and continuum states and, therefore, an extensive region of space to be sampled during the calculation. As a consequence, direct simulations of photoionization processes are currently only feasible for systems containing up to three electrons. Despite this fundamental restriction, many physical effects can be essentially described by single- and two-electron models, among them are high-order harmonic generation and non-sequential double-ionization of atoms and molecules. A plethora of numerical investigations have been performed on atomic and molecular hydrogen and helium in the last two decades, and these have had a strong impact on the current understanding of photoionization. On the other hand, there are processes which are characterized by the interplay of a larger number of electrons, such as tunnel ionization, the Auger effect and, to give a more recent example, the temporal delay between the photo-emission of electrons from different shells of neon and krypton. The many-electron character of these effects complicates the accurate, time-resolved simulation and, so far, no universally applicable method exists. This review presents two theoretical methods which are promising candidates for closing this gap–the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method and the time-dependent restricted active space configuration interaction (TD-RASCI) method. Both represent the wavefunction in a linear subspace of the many-body Hilbert space and follow particular strategies to avoid the exponential problem. This makes it possible to treat a much larger number of electrons than with the direct techniques mentioned above

Short communication: Use of genomic and metabolic information as well as milk performance records for prediction of subclinical ketosis risk via artificial neural networks

Subclinical ketosis is one of the most prevalent metabolic disorders in high-producing dairy cows during early lactation. This renders its early detection and prevention important for both economical and animal-welfare reasons. Construction of reliable predictive models is challenging, because traits like ketosis are commonly affected by multiple factors. In this context, machine learning methods offer great advantages because of their universal learning ability and flexibility in integrating various sorts of data. Here, an artificial-neural-network approach was applied to investigate the utility of metabolic, genetic, and milk performance data for the prediction of milk levels of β-hydroxybutyrate within and across consecutive weeks postpartum. Data were collected from 218 dairy cows during their first 5wk in milk. All animals were genotyped with a 50,000 SNP panel, and weekly information on the concentrations of the milk metabolites glycerophosphocholine and phosphocholine as well as milk composition data (milk yield, fat and protein percentage) was available. The concentration of β-hydroxybutyric acid in milk was used as target variable in all prediction models. Average correlations between observed and predicted target values up to 0.643 could be obtained, if milk metabolite and routine milk recording data were combined for prediction at the same day within weeks. Predictive performance of metabolic as well as milk performance-based models was higher than that of models based on genetic information