A comparative study of time dependent quantum mechanical wave packet evolution methods

Truong, Thanh N.; Tanner, John J.; Bała, Piotr; McCammon, J. Andrew; Kouri, Donald J.; Lesyng, Bogdan; Hoffman, David K.

doi:10.1063/1.462870

Cited by 74 publications

(37 citation statements)

References 86 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The equations are, nevertheless, identical, and experience from this field may be translated to others. We learned from Kosloff's review, 4 from the work of Lubich and co-workers, [5][6][7] from the comparisons of Truong and others, 8 and from other references that will be cited when appropriate. For the particular problem of TDDFT, we would like to mention the recent work of Sugino and Miyamoto.…”

Section: ͑6͒mentioning

confidence: 99%

See 1 more Smart Citation

Propagators for the time-dependent Kohn–Sham equations

Castro

Marques

Rubio

2004

The Journal of Chemical Physics

515

449

View full text Add to dashboard Cite

In this paper we address the problem of the numerical integration of the time-dependent Schrödinger equation i‫ץ‬ t ϭĤ . In particular, we are concerned with the important case where Ĥ is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, Ĥ is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: ͑i͒ First, we look at several algorithms to approximate exp(Â ), where Â is a time-independent operator ͓e.g., Â ϭϪi⌬tĤ () for some given time ͔. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. ͑ii͒ We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem ͑ii͒ is not equivalent to ͑i͒. All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations.

show abstract

Section: ͑6͒mentioning

confidence: 99%

“…3 we plot the error in the dipole moment, after performing a single step propagation, Û (⌬t,0). The system under consideration is a Na 8 cluster in the jellium model, excited from its ground state by a laser pulse of frequency 2 Hartree. The fourth-order method is, as expected, more precise.…”

Section: F Performance Comparisonsmentioning

confidence: 99%

Propagators for the time-dependent Kohn–Sham equations

Castro

Marques

Rubio

2004

The Journal of Chemical Physics

515

449

View full text Add to dashboard Cite

show abstract

“…Basic improvement in algorithms for solving the timedependent Schroödinger equation can therefore impact many areas of basic research. Among numerical techniques developed for solving the time-dependent Schrödinger equation [1][2][3] (see T. N. Truong et al [4] for earlier references), the method of split-operator [2], or its higher order variant, the method of symplectic integrator [5][6][7], has the advantage of being unitary, remain applicable in higher dimensions and easily generalizable to higher order. The disadvantage is that the time step size needed for convergence seemed to be small and many iterations are required for evolving system forward in time.…”

Section: Introductionmentioning

confidence: 99%

Fourth order gradient symplectic integrator methods for solving the time-dependent Schrödinger equation

Chin

Chen

2001

The Journal of Chemical Physics

View full text Add to dashboard Cite

We show that the method of splitting the operator e ǫ(T +V ) to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schrödinger equation. These algorithms require knowing the potential and the gradient of the potential. One 4th order algorithm only requires four Fast Fourier Transformations per iteration. In a one dimensional scattering problem, the 4th order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Ruth-Forest symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to 6th order also produced better converged algorithms than iterating the Ruth-Forest algorithm to 6th order or using Yoshida's 6th order algorithm A directly.

show abstract

“…At short distances, where the process of charge exchange is significant, the Perturbation Theory is not applicable and more exact methods must be implemented. Among the most widely-used quantum methods are the Complex Scaling [1,2], the Stabilization Method [3,4] and the Wave-packet Propagation Method [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Semi‐classical calculation of resonant states of a charged particle interacting with a metallic surface

Zuluaga

Mahecha²,

Chulkov

2005

Physica Status Solidi (b)

View full text Add to dashboard Cite

PACS 68.47. De, 73.20.At, We assess the applicability of the semi-classical approach of Herman -Kluk with filter diagonalization to determine resonant states of either the electron-surface system or the ion-surface system. An effective potential model of the interaction of an electron with a ruthenium metallic surface is used. The evolution of the wave-function and the resonant states of this system are calculated. Analogous results for the interaction of the system formed by the H -and the ruthenium surface are presented. For the calculation of the resonances, the semi-classical wave-function is found, and the autocorrelation function between the initial and final wave-functions is calculated, from which the position and width of the resonances are extracted by using the harmonic inversion by filter diagonalization. The results are compared with results available in the literature for similar models obtained by quantum calculations using fast Fourier Transform. The positions of the lower-lying resonances found with the semi-classical and quantum approaches match closely, while the values of the widths of the resonances show larger discrepancies.

show abstract

A comparative study of time dependent quantum mechanical wave packet evolution methods

Cited by 74 publications

References 86 publications

Propagators for the time-dependent Kohn–Sham equations

Propagators for the time-dependent Kohn–Sham equations

Fourth order gradient symplectic integrator methods for solving the time-dependent Schrödinger equation

Semi‐classical calculation of resonant states of a charged particle interacting with a metallic surface

Contact Info

Product

Resources

About