Quantum wavepacket dynamics with trajectories: wavefunction synthesis along quantum paths

Wyatt, Róbert E.

doi:10.1016/s0009-2614(99)00921-5

Cited by 126 publications

(85 citation statements)

References 17 publications

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“…If done appropriately, such a decomposition can lead to very important ramifications for quantum trajectory methods (QTMs) 5,6,7,8,9,10,11,12,13,14 -i.e., trajectorybased numerical techniques for performing exact quantum dynamics calculations, based on Bohmian mechanics 15,16,17,18,19,20 -due to nonlinearity of the Bohmian equations of motion. In particular, the earlier series of articles has culminated in a set of trajectorybased time-dependent methods for computing stationary scattering quantities (the theoretical underpinning of all chemical reactions) in one degree of freedom (DOF).…”

Section: Introductionmentioning

confidence: 99%

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Development and Numerical Analysis of "Black-Box" Counterpropagating Wave Algorithm for Exact Quantum Scattering Calculations

Poirier

2007

J. Theor. Comput. Chem.

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] a bipolar counter-propagating wave decomposition, Ψ = Ψ+ + Ψ−, was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ± approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Ψ has many nodes, or is wildly oscillatory. In this paper, the earlier results are used to construct a universal "black-box" algorithm, numerically robust, stable and efficient, for computing accurate scattering quantities of any quantum dynamical system in one degree of freedom.

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Section: Introductionmentioning

confidence: 99%

“…(7) via Eq. (8). Obtaining r ∓k = |Ψ ∓k | is straightforward; however, s ∓k =h arctan (ImΨ ∓k /ReΨ ∓k ) requires special care in the choice of branch cut, to ensure continuity of the field function throughout the coordinate range.…”

mentioning

confidence: 99%

Development and Numerical Analysis of "Black-Box" Counterpropagating Wave Algorithm for Exact Quantum Scattering Calculations

Poirier

2007

J. Theor. Comput. Chem.

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“…Finally, the concept of bundles of trajectories that form a flux tube is found to remain valid in a quantum-mechanical formulation 26 that will be discussed in Sec. VIII.…”

Section: Reactive Cylinders In Phase Spacementioning

confidence: 99%

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

Lorquet

2015

The Journal of Chemical Physics

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The purpose of the present work is to determine initial conditions that generate reacting, recrossingfree trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of this series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet. C 2015 AIP Publishing LLC. [http://dx

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“…The number density n is given by a superposition of δ− functions in physical space of which the third derivative has to be computed to evaluate the force. This can be either done by computing n on a mesh using the usual cloud in cell approach and then using a difference discretization, or by computing the third derivatives directly in a meshless approach [32] , [33]. The first approach requires a considerable amount of smoothing.…”

Section: Effective Potentials and Particle Discretizationsmentioning

confidence: 99%

Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach

Ringhofer

Gardner

Vasileska

2003

Int. J. Hi. Spe. Ele. Syst.

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We present a thermodynamic approach to introducing quantum corrections to the classical transport picture in semiconductor device simulation. This approach leads to a modified Boltzmann equation with a quantum corrected force term and to quantum corrected fluid, or quantum hydrodynamic models. We present the quantum interaction of electrons with a gate oxide barrier potential and quantum hydrodynamic simulations of a resonant tunneling diode as application examples.

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Quantum wavepacket dynamics with trajectories: wavefunction synthesis along quantum paths

Cited by 126 publications

References 17 publications

Development and Numerical Analysis of "Black-Box" Counterpropagating Wave Algorithm for Exact Quantum Scattering Calculations

Development and Numerical Analysis of "Black-Box" Counterpropagating Wave Algorithm for Exact Quantum Scattering Calculations

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach

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