Multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms

Numerical simulations present an indispensable way to the understanding of physical processes. In quantum mechanics, where the theoretical description is given in terms of the time-dependent Schrödinger equation (TDSE), the road is, however, difficult for any but the simplest systems. This is particularly true if one considers photoionization processes of atoms and mole\-cules, 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 composed of up to three particles. Despite this fundamental restriction, many physical effects can be essentially described by single- and two-electron models, among them high-order harmonic generation and non-sequential double-ionization of atoms and mole\-cules. 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 hence, no universally applicable method exists. The present work develops 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 previously. The MCTDHF method is already well established in the scientific community, but has been applied only rarely to photoionization processes so far. On the other hand, the TD-RASCI method is an original contribution, and is applied for the first time to solutions of the time-dependent Schrödinger equation. Further, through the invention of appropriate, grid-like single-particle basis sets, we adjust these general approaches to efficiently treat photoionization processes in many-electron atoms and molecules. After their thorough introduction, the MCTDHF and the TD-RASCI method are applied to several topics of photoionization physics. Among them is, first, the problem of calculating cross sections of atoms, for which we particularly consider helium, beryllium and neon. In most parts, this is accomplished for the first time in the framework of the developed methods. Next, we consider the two-photon double-ionization of helium, which has attracted considerable interest in recent years, and perform simulations with the MCTDHF method. We further apply the TD-RASCI method to study two-color pump-probe process in beryllium, the simulation of which requires an explicitly time-dependent treatment. We find that both methods are highly appropriate for accurately describing correlated single-ionization processes. Moreover, the TD-RASCI method is able to model relevant doubly-excited states, which are of central importance for a variety of physical processes.Trotz dieser fundamentalen Einschränkung lassen sich viele physikalische Effekte bereits durch Ein- und Zweiteilchenmodelle beschreiben, darunter zum Beispiel die Erzeugung höherer Harmonischer oder die nicht-sequentielle Doppelionisation. In diesem Sinne wurde in den letzten zwei Jahrzehnten eine Vielzahl numerischer Untersuchungen an atomarem und molekularem Wasserstoff sowie Helium unternommen, welche einen starken Einfluss auf das momentane Verständnis von Photoionisations-Prozessen nahmen. Andererseits gibt es jedoch physikalische Effekte, die durch das Zusammenwirken einer größeren Anzahl von Elektronen gekennzeichnet sind, etwa die Tunnel-Ionisation, der Auger-Effekt oder die kürzlich entdeckte zeitliche Verzögerung in der Emission von Elektronen aus verschiedenen atomaren Schalen von Neon und Krypton. Der immanente Vielteilchencharakter macht die zeitaufgelöste Simulation dieser Prozesse zu einer schwierigen Aufgabe, für die es bisher keine universell einsetzbare und gleichzeitig akkurate Methode gibt. In dieser Arbeit werden zwei theoretische Methoden zur Simulation von Photoionisations-Prozessen von Vielteilchenatomen und -molekülen vor\-gestellt, die vielversprechende Kandidaten zur Schließung dieser vorhandenen Lücke darstellen, nämlich die zeitabhängige Multikonfigurations-Hartree-Fock (MCTDHF) Methode sowie die zeitabhängige restricted-active-space Konfigurations-Wechselwirkungsmethode (TD-RASCI). Beide stellen die quantenmechanische Wellenfunktion in einem linearen Unterraum des Vielteilchen-Hilbertraumes dar und folgen dabei speziellen Ansätzen um das Problem des exponentiellen Wachstums zu vermeiden. Dadurch kann eine weitaus größere Teilchenzahl als mit der zuvor erwähnten direkten Technik simuliert werden. Weiterhin werden diese zunächst sehr allgemeinen Methoden durch den Gebrauch geeigneter Basissätze auf die effiziente Beschreibung von Photoionisations-Prozessen optimiert. Nach ihrer Einführung werden die MCTDHF und TD-RASCI Methode auf aktuelle Themen der Photoionisations-Physik angewandt. Zunächst wenden wir uns der Berechnung von Ionisations-Streuquerschnitten der Atome Helium, Beryllium und Neon zu, welche weitgehend zum ersten Male mithilfe der eingeführten Methoden untersucht wird. Des Weiteren studieren wir die Zwei-Photonen-Ionisation von Helium, der in jüngerer Zeit großes theoretisches Interesse zukam, mithilfe von Simulationen mit der MCTDHF Methode. Als grundlegendes Beispiel eines explizit zeitabhängigen Prozesses wird darüberhinaus die Pump-Probe Ionisation von Beryllium betrachtet. Unsere Untersuchungen zeigen, dass sowohl die MCTDHF Methode als auch die TD-RASCI Methode die Einelektronen-Photoionisation akkurat zu beschreiben vermag. Mithilfe der TD-RASCI Methode ist es zudem möglich, selektierte doppelt-angeregte Zustände in die Rechnung zu integrieren, welche eine zentrale Rolle bei einer Vielzahl physikalischer Prozesse spielen

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

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

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 Schrödinger equation we present results for N = 4,6 from multiconfiguration time-dependent Hartree-Fock simulations

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 ionization from the groundstate for photon energies in the non-sequential regime, and compare them to direct solutions of the Schr\"odinger equation using the time-dependent (full) Configuration Interaction method (TDCI). We find that the single-ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI

Quantum Breathing Mode of Interacting Particles in a One-dimensional Harmonic Trap

Extending our previous work, we explore the breathing mode---the [uniform] radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from the ideal quantum to the classical regime and confirm that it is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles

Time-dependent restricted active space Configuration Interaction for the photoionization of many-electron atoms

We introduce the time-dependent restricted active space Configuration Interaction method to solve the time-dependent Schr\"odinger equation for many-electron atoms, and particularly apply it to the treatment of photoionization processes in atoms. The method is presented in a very general formulation and incorporates a wide range of commonly used approximation schemes, like the single-active electron approximation, time-dependent Configuration Interaction with single-excitations, or the time-dependent R-matrix method. We proof the applicability of the method by calculating the photoionization cross sections of Helium and Beryllium, as well as the X-ray--IR pump-probe ionization in BerylliumComment: 12 pages, 9 figure

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

International audienceAbstractBackgroundRecently, 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