Fast Fourier Transform Simulation Techniques for Coulomb Gases

An improved approach to updating the electric field in simulations of Coulomb gases using the local lattice technique introduced by Maggs and Rossetto, is described and tested. Using the Fast Fourier Transform (FFT) an independent configuration of electric fields subject to Gauss' law constraint can be generated in a single update step. This FFT based method is shown to outperform previous approaches to updating the electric field in the simulation of a basic test problem in electrostatics of strongly correlated systems.Comment: 5 pages, 3 figure

A wave packet Golden Rule treatment of vibrational predissociation

The time-dependent wave packet technique is applied to the Golden Rule treatment of vibrational predissociation. The wave packet at time zero is taken as the product of the quasibound wave function and the coupling inducing predissociation. The rate for vibrational predissociation can then be obtained by Fourier transform into the energy domain of the time-dependent wave packet autocorrelation function. The method has been applied to a model triatomic van der Waals molecule. It is shown that when the bound-state components of the wave packet are projected out, the time-dependent version of the Golden Rule approximation provides an alternative efficient technique to treat intramolecular decay. © 1991 American Institute of Physics.Peer Reviewe

Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation

We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the so-called standard discrete path integral methods is derived by direct discretization of the Feynman-Kac formula. Second, we consider a particular random series technique based upon the Levy-Ciesielski representation of the Brownian bridge and analyze its main implementations, namely the primitive, the partial averaging, and the reweighted versions. It is shown that the n=2^k-1 subsequence of each of these methods can also be interpreted as a discrete path integral method with appropriate short-time approximations. We therefore establish a direct connection between the discrete and the random series approaches. In the end, we give sharp estimates on the rates of convergence of the partial averaging and the reweighted Levy-Ciesielski random series approach for sufficiently smooth potentials. The asymptotic rates of convergence are found to be O(1/n^2), in agreement with the rates of convergence of the best standard discrete path integral techniques.Comment: 20 pages, 4 figures; the two equations before Eq. 14 are corrected; other typos are remove

Some aspects of the Liouville equation in mathematical physics and statistical mechanics

This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem. Furthermore, we have implied on the formal frame work of Stochastic Liouville equation (SLE)

Application of the time-dependent Hartree grid-configuration interaction method to the desorption of diatomic molecules from solid surfaces

We study UV laser induced photodesorption of diatomic molecules from solid surfaces by means of the time-dependent Hartree grid-configuration interaction (TDHG-CI) method [J. Chem. Phys. 93, 4740 (1990)]. Converged partial and total absorption cross sections are computed in several cases to demonstrate the flexibility and accuracy of the method. Comparison to TDHG results without CI corrections is also made. The failure of simple TDHG dynamics to reproduce state resolved rotational cross sections in various strong coupling limits is noted as a justification for the development of TDHG-CI algorithms. © 1993 American Institute of Physics.This work was partially supported by EEC Grant No. SC1.l45.C. RDC acknowledges financial support from the National Science Foundation, Grant No. CHE-9101432, and the Camille and Henry Dreyfus Foundation.Peer Reviewe

Beyond the time-dependent Hartree grid approximation for curve-crossing problems

A new >configuration-interaction> method is presented which extends the single-surface time-dependent Hartree grid (TDHG) approximation into a formally exact algorithm for obtaining multidimensional quantum wave-packet dynamics on nonradiatively coupled electronic potential surfaces. As a numerical example, photofragmentation cross sections are computed for a two-degree-of-freedom model of direct dissociation. For systems prepared in vibrationally excited states of the ground electronic potential the TDHG approximation fails due to >direct correlation> effects, while our method provides accurate results. © 1992 American Institute of Physics.J. C.-M. gratefully acknowledges a grant from the Ministerio de Educacion y Ciencia of Spain and the Fulbright Comission. R. D. C. wishes to thank the National Science Foundation (Grant No. CHE-9101432), the Donors of the Petroleum Research Fund, administered by the American Chemical Society and the Camille and Henry Dreyfus Foundation for financial support, and the Pittsburgh Supercomputing Center where many of the calculations were carried out.Peer Reviewe

Application of a coupled-surface time-dependent Hartree grid method to excited state optical spectroscopy

The dynamics of multidimensional wave packet motion on nonadiabatically coupled electronic potential surfaces is explored by numerically exact time¿dependent quantum mechanics and by the time¿dependent Hartree grid (TDHG) approximation. Excellent agreement is found between the TDHG and the exact evolution of the wave packet; in particular, the approximation yields accurate total cross sections for electronic absorption, excitation profiles for resonance Raman scattering, and partial cross sections for photofragmentation in a two degree of freedom model of direct dissociation (which is qualitatively related to experimentally observed processes in methyl halides and ICN).@ American Institute of PhysicsThis work was supported by a grant from the National Science Foundation, the Petroleum Research Fund, the Alfred P. Sloan Foundation, and the Camille and Henry Dreyfus Foundation. J. C.-M. gratefully acknowledges a grant from the Ministerio de Educacion y Ciencia of SpainPeer Reviewe

Adding configuration interaction to the time-dependent Hartree Grid Approximation

The time‐dependent Hartree grid (TDHG) method is extended into an ab initio algorithm for obtaining exact quantum wave packet dynamics. The new algorithm employs a superposition of orthogonal zeroth order time‐dependent basis functions generated from a single TDHG wave packet trajectory. The superposition coefficients are themselves time‐dependent, and are responsible for mixing the basis functions in such a way as to represent exact solutions of the time‐dependent Schrodinger equation. Evolution of the superposition coefficients is governed by a set of first‐order linearly coupled ordinary differential equations. The couplings between coefficients are given by matrix elements of a naturally identified interaction potential taken between members of the zeroth order basis. In numerical tests involving computation of S‐matrix elements for collinear inelastic atom–Morse oscillator scattering the method proves accurate, flexible and efficient, and appears to be easily extendable to more complicated systems.J.C-M. gratefully acknowledges a grant from the Ministerio de Educacion y Ciencia of Spain and the Fullbright CommissionPeer Reviewe

Lifetimes of selective-adsorption resonances in atom-surface elastic scattering

10 pags. ; 6 figs. ; 4 tabs.From a time-dependent calculation and by assuming an exponential decay law for the resonances formed, we have computed lifetimes of selective-adsorption resonances (SAR’s) in the elastic scattering of He atoms from the Cu(110) and Cu(117) surfaces. In previous works, where SAR’s were studied within the time-independent close-coupling method, we found that in addition to the energy width obtained by analyzing plots of diffraction intensities versus the energy of the incident beam, another internal energy width (with a very different numerical value) can be defined. Here we show that it is this internal width that can be directly related to the lifetime of the resonance. Also, we have performed a simulation of the half collision or ‘‘selective-desorption’’ process. This approach is shown to yield accurate values for lifetimes of SAR’s. © 1994 The American Physical SocietyThis work has been partially supported by the CICYT Grant No. PB87-0272 and Comunidad de Madrid Grant No. 064/92. R.D.C. wishes to acknowledge National Science Foundation Grant No. CHE-9101432 for partial financial support.Peer reviewe