On the role of parallel architecture supercomputers in time-dependent approaches to quantum scattering

Hoffman, David K.; Sharafeddin, Omar A.; Kouri, Donald J.; Carter, Michael; Nayar, Naresh; Gustafson, John L.

doi:10.1007/bf01113698

Cited by 8 publications

(2 citation statements)

References 55 publications

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“…For an initial Gaussian wavepacket, very accurate results, with a reasonably low M, can be obtained using a cr(0) which is about 10-20 times smaller than the initial width of the Gaussian wavepacket. The discretized version of eq 3 is easily obtained by introducing a trapezoidal quadrature for the integration over x', yielding1 nxj\t) = g(x,)Ax t FM{xJ,xf\T)Q*(xr)-'nxf\t -t) (8) In the present calculation we choose Ax so that *K0)/A(x) > 3 (9) i.e., we take at least three quadrature points under each DAF.…”

Section: Distributed Approximating Functionsmentioning

confidence: 99%

A computational demonstration of the distributed approximating function approach to real time quantum dynamics

Nayar¹,

Hoffman²,

Ma³

et al. 1992

J. Phys. Chem.

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We report computational applications of the newly developed distributed approximating function (DAF) approach to real time quantal wavepacket propagation for several one-dimensional model problems. The DAF is constructed to fit all wavepackets accurately which can be represented, to the same accuracy, by a polynomial of degree M, or less, within the envelope of the DAF. (This defines the "DAF class" of functions.) By expressing the DAF (and thus the wavepacket to be propagated) in terms of Hermite functions (Each a product of a Hermite polynomial and its Gaussian generating function), the DAF approximation to the wavepacket is propagated freely and exactly for a short time 7 . The Hermite functions are the natural basis states for describing the free evolution of a localized particle and yield a highly banded representation for the free particle propagator. Combining the DAF class free propagation scheme with any of several short time approximations to the full propagator enables one to propagate the wavepacket through a potential. The DAF results for the propagated wavepacket and various scattering amplitudes are shown to be in good agreement with those obtained by more standard methods.

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Section: Distributed Approximating Functionsmentioning

confidence: 99%

A computational demonstration of the distributed approximating function approach to real time quantum dynamics

Nayar¹,

Hoffman²,

Ma³

et al. 1992

J. Phys. Chem.

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“…Then the computational effort required to apply this discrete propagator matrix to the appropriate discrete wave packet "vector" is greatly reduced, while at the same time retaining an optimal form for implementation on massively parallel computers. 4 It was noted that the possibility of banding the discretized free propagator matrix depended on the recognition that any physically realizable system always involved a decay in the contribution made by increasingly large magnitude momenta. 5 This was first noted by Makri6 earlier in the context of the Feynman path integral7" 18 where the x to x' propagator oscillates with a frequency proportional to (x'-x) (for short real times) is nonzero over the entire…”

Section: Introductionmentioning

confidence: 99%

Toward a new time-dependent path integral formalism based on restricted quantum propagators for physically realizable systems

Kouri¹,

Hoffman²

1992

J. Phys. Chem.

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Various mathematical properties of the exact free and full short-real-time propagators in the coordinate representation are discussed. The viewpoint is emphasized that these properties, which prevent the use of the exact path integral formalism as a basis for straightforward computations and result in bizarre behavior wholly at odds with our (macr~pically conditioned) intuition, are neuer relevant, in connection with any experimentally realizable system. These computationally disasterous mathematical properties of the kinetic energy part of the propagator may be removed by means of restricting the wave packets which will be propagated to L2 functions which can be fitted, sufficiently accurately, by a polynomial of a specific degree within the envelope of the fitting function. This is an example of 'prefiltering" oscillations whose frequency increases without bound (i.e., as the distance Ix'-XI travelled in short time T ) . The decay in the kinetic energy, which characterizes any physically realizable system, has been achieved using our continuum distributed approximating functions, which limit the class of wave packets which can be propagated. We also discuss the role of the potential energy. Again, difficulties arise which could be addressed by potential energy cutoff procedures. However, the more desireable possibility of developing a smoothly prefiltered full propagator is pointed out.

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High Performance Computing in Computational Chemistry: Methods and Machines

Kendall

Harrison

Littlefield

et al. 1995

Reviews in Computational Chemistry

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On the role of parallel architecture supercomputers in time-dependent approaches to quantum scattering

Cited by 8 publications

References 55 publications

A computational demonstration of the distributed approximating function approach to real time quantum dynamics

A computational demonstration of the distributed approximating function approach to real time quantum dynamics

Toward a new time-dependent path integral formalism based on restricted quantum propagators for physically realizable systems

High Performance Computing in Computational Chemistry: Methods and Machines

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