Explicit schemes for time propagating many-body wavefunctions

Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical solution of the time-dependent Schr\"odinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first order differential equations that are characterized by a high degree of stiffness. We analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy however differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. We consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness. For the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.Comment: 24 pages, 14 Figure

Multiresolution schemes for time-scaled propagation of wave packets

We present a detailed analysis of the time scaled coordinate approach and its implementation for solving the time-dependent Schr\"odinger equation describing the interaction of atoms or molecules with radiation pulses. We investigate and discuss the performance of multi-resolution schemes for the treatment of the squeezing around the origin of the bound part of the scaled wave packet. When the wave packet is expressed in terms of B-splines, we consider two different types of breakpoint sequences: an exponential sequence with a constant density and an initially uniform sequence with a density of points around the origin that increases with time. These two multi-resolution schemes are tested in the case of a one-dimensional gaussian potential and for atomic hydrogen. In the latter case, we also use Sturmian functions to describe the scaled wave packet and discuss a multi-resolution scheme which consists in working in a sturmian basis characterized by a set of non-linear parameters. Regarding the continuum part of the scaled wave packet, we show explicitly that, for large times, the group velocity of each ionized wave packet goes to zero while its dispersion is suppressed thereby explaining why, eventually, the scaled wave packet associated to the ejected electrons becomes stationary. Finally, we show that only the lowest scaled bound states can be removed from the total scaled wave packet once the interaction with the pulse has ceased

Interaction Of Electrons With Spin Waves In The Bulk And In Multilayers

The exchange interaction between electrons and magnetic spins is considerably enhanced near interfaces, in magnetic multilayers. As a result, a dc current can be used to generate spin oscillations. We review theory and experimental evidence. The s-d exchange interaction causes a rapid precession of itinerant conduction-electron spins s around the localized spins S of magnetic electrons. Because of the precession, the time-averaged interaction torque between s and S vanishes. An interface between a magnetic layer and a spacer causes a local coherence between the precession phases of differnt electrons, within 10 nm from the interface, and restores the torque. Also, a second magnetic layer with pinned S is used to prepare s in a specific direction. the current-induced drive torque of s on S in the active layer may be calculated from the spin current (Slonczewski) or from the spin imbalance Delta-mu (Berger). Spin current and Delta-mu are proportional to each other, and can arise from Fermi-surface translation, as well as from expansion/contraction.Comment: Invited paper at Seattle MMM01 Conference, Nov. 2001 (to appear in J. Appl. Phys.

Spectral data for doubly excited states of helium with non-zero total angular momentum

A spectral approach is used to evaluate energies and widths for a wide range of singlet and triplet resonance states of helium. Data for total angular momentum $L=1,...,4$ is presented for resonances up to below the 5th single ionization threshold. In addition the expectation value of $\cos(\theta_{12})$ is given for the calculated resonances.Comment: 35 pages, 16 tables, to be published in Atomic Data and Nuclear Data Table

Two--Electron Atoms in Short Intense Laser Pulses

We discuss a method of solving the time dependent Schrodinger equation for atoms with two active electrons in a strong laser field, which we used in a previous paper [A. Scrinzi and B. Piraux, Phys. Rev. A 56, R13 (1997)] to calculate ionization, double excitation and harmonic generation in Helium by short laser pulses. The method employs complex scaling and an expansion in an explicitly correlated basis. Convergence of the calculations is documented and error estimates are provided. The results for Helium at peak intensities up to 10^15 W/cm^2 and wave length 248 nm are accurate to at least 10 %. Similarly accurate calculations are presented for electron detachment and double excitation of the negative hydrogen ion.Comment: 14 pages, including figure

Modelling laser-atom interactions in the strong field regime

We consider the ionisation of atomic hydrogen by a strong infrared field. We extend and study in more depth an existing semi-analytical model. Starting from the time-dependent Schroedinger equation in momentum space and in the velocity gauge we substitute the kernel of the non-local Coulomb potential by a sum of N separable potentials, each of them supporting one hydrogen bound state. This leads to a set of N coupled one-dimensional linear Volterra integral equations to solve. We analyze the gauge problem for the model, the different ways of generating the separable potentials and establish a clear link with the strong field approximation which turns out to be a limiting case of the present model. We calculate electron energy spectra as well as the time evolution of electron wave packets in momentum space. We compare and discuss the results obtained with the model and with the strong field approximation and examine in this context, the role of excited states.Comment: 11 pages, 5 figure

Strong field approximation within a Faddeev-like formalism for laser-matter interactions

We consider the interaction of atomic hydrogen with an intense laser field within the strong-field approximation. By using a Faddeev-like formalism, we introduce a new perturbative series in the binding potential of the atom. As a first test of this new approach, we calculate the electron energy spectrum in the very simple case of a photon energy higher than the ionisation potential. We show that by contrast to the standard perturbative series in the binding potential obtained within the strong field approximation, the first terms of the new series converge rapidly towards the results we get by solving the corresponding time-dependent Schroedinger equation.Comment: 7 pages, 1 figur

Circular Rydberg Orbits in Circularly Polarized Microwave-radiation

Using classical dynamics we analyze the ionization of the maximum angular-momentum circular Rydberg orbits of the hydrogen atom in strong circularly polarized microwave radiation. We find the ionization threshold generally higher than that for the static field, depending upon the direction of rotation, and in some cases completely different than the prediction based upon the above barrier escape. Below the ionization threshold the system returns to its initial state after interacting with the smooth microwave pulse

Norm of the Wave-function On a Complex Basis

When the wave function of a system which breaks up is represented on a complex basis, the norm of the wave function, if evaluated as a direct sum over the basis, remains unity only for as long as the continuum is not significantly populated. However, we show that if the norm is evaluated by Pade summation, it remains unity until one of the fragments leaves the region spanned by the basis; subsequently the norm drops to a value that is simply the probability for the system not to break up, i.e., to remain intact. The probability for breakup into a particular channel must be calculated before the ''critical'' time at which the norm drops. These remarks, and others, are illustrated numerically for the case of a hydrogen atom that is photoionized by a short pulse of light