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

Discrete sets of Sturmian functions applied to two-electron atoms

We present a configuration-interaction (CI) method based on Sturmian functions. The components of this CI basis are the solutions of a two-body Sturmian eigenproblem, where the eigenvalues are related to the interacting potential in the two-body equation. Our method accommodates any arbitrary, physically sound, central potential in the Sturmian equations and different adequate asymptotic conditions. Computation of eigenvalues and eigenfunctions is performed by direct numerical discretization of the Sturmian equation. We apply this method to obtain bound states for two-electron systems. We show the convergence of the partial-wave expansion for the ground-states energies of the He atom and the H- ion, and obtain very accurate results that are compared with other recent CI calculations.Fil: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energí­a Atómica. Gerencia del Area Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Balseiro). División Colisiones Atómicas; ArgentinaFil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energí­a Atómica. Gerencia del Area Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Balseiro). División Colisiones Atómicas; ArgentinaFil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energí­a Atómica. Gerencia del Area Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Balseiro). División Colisiones Atómicas; ArgentinaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentin

Generalized Sturmians in the time-dependent frame: effect of a fullerene confining potential

In this work we present a novel implementation of the Generalized Sturmian Functions in the time-dependent frame to numerically solve the time-dependent Schrödinger equation. We study the effect of the confinement of H atom in a fullerene cage for the 1s → 2p resonant transition of the atom interacting with a finite laser pulse, calculating the population of bound states and spectral density

Electron impact single ionization of the He-isoelectronic sequence

In this work, triply differential cross sections for single electron emission due to electron impact on the He-isoelectronic sequence are calculated by using a Born-C3 model. The influence of the nuclear charge on the angular distributions is analyzed. The validity of a scaling law initially derived in the framework of photo-double-ionization is discussed.Fil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Rodriguez, Karina Viviana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Otranto, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentin

Inertial Movements of the Iris as the Origin of Postsaccadic Oscillations

Recent studies on the human eye indicate that the pupil moves inside the eyeball due to deformations of the iris. Here we show that this phenomenon can be originated by inertial forces undergone by the iris during the rotation of the eyeball. Moreover, these forces affect the iris in such a way that the pupil behaves effectively as a massive particle. To show this, we develop a model based on the Newton equation on the noninertial reference frame of the eyeball. The model allows us to reproduce and interpret several important findings of recent eye-tracking experiments on saccadic movements. In particular, we get correct results for the dependence of the amplitude and period of the postsaccadic oscillations on the saccade size and also for the peak velocity. The model developed may serve as a tool for characterizing eye properties of individuals.Fil: Bouzat, Sebastian. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Freije, María Luján. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentin

Sturmian expansions for two-electron atomic systems: Singly and doubly excited states

We present a configuration interaction (CI) method based on the Sturmian expansion for bound states of a two-electron atomic system. These Sturmian functions are solutions of one-electron quantum mechanical problems, where the eigenvalue is the magnitude of a short-range potential. Also, they fulfill the long-range boundary conditions of Coulomb potentials. We choose to expand the Sturmians of the CI basis using L2 Laguerre-type functions. We compute ground and single-excited states energies for He and H. Moreover, we are able to obtain energies and widths of double excited states of He, using a Sturmian basis with outgoing boundary conditions. In all cases, our ansatz outperforms other CI calculations, for similar basis size. © 2010 The American Physical Society.Fil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Física; ArgentinaFil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin

Sturmian functions in a L2 basis: critical nuclear charge for n-electron atoms

Two particle Sturmian functions [M. Rotenberg, Ann. Phys., NY 19 (1962) 262; S.V. Khristenko, Theor. Math. Fiz. 22 (1975) 31 (Engl. Transl. Theor. Math. Phys. 22, 21)] for a short range potentials are obtained by expanding the solution of the Schrodinger equation in a finite ¨ L2Laguerretype basis. These functions are chosen to satisfy certain boundary conditions, such as regularity at the origin and the correct asymptotic behavior according to the energy domain: exponential decay for negative energy and outgoing (incoming or standing wave) for positive energy. The set of eigenvalues obtained is discrete for both positive and negative energies. This Sturmian basis is used to solve the Schrodinger equation for ¨ a one-particle model potential [A.V. Sergeev, S. Kais, J. Quant. Chem. 75 (1999) 533] to describe the motion of a loosely bound electron in a multielectron atom. Values of the two parameters of the potential are computed to represent the Helium isoelectronic series and the critical nuclear charge Zc is found, in good agreement with previous calculations.Fil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Colavecchia, Flavio Dario. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

Theory of Hyperspherical Sturmians for Three-Body Reactions

In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied by means of the Schro ̈dinger equation in hyperspherical coordinates. The three-body wave function is written as a sum of two terms. The first one defines the initial channel of the collision while the second one describes the scattered wave, which contains all the information about the collision process. The dynamics is ruled by an nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions. A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products of angular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and the nonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrix methods. To be able to deal with general systems, discretization schemes are proposed to solve the angular and radial Sturmian equations. This procedure allows these discrete functions to be connected with the hyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptotic limit of the scattered wave function.Fil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); ArgentinaFil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); ArgentinaFil: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentin