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University of South Carolina

Correlation functions

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Full-Text Articles in Physics

Wavepacket Approach To The Cumulative Reaction Probability Within The Flux Operator Formalism, Sophya V. Garashchuk, T. Vazhappilly Jan 2009

Wavepacket Approach To The Cumulative Reaction Probability Within The Flux Operator Formalism, Sophya V. Garashchuk, T. Vazhappilly

Faculty Publications

Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Diracδ-function representable as a localized Gaussian wavepacket. This functional form enables computation of the cumulative reaction probability N(E) from the wavepacket time-correlation functions. The Gaussian based form of the flux eigenfunctions, which is not tied to a finite basis of a quantum-mechanical calculation, is particularly useful for approximate calculation of N(E) with the trajectory based wavepacket propagation techniques. Numerical illustration is given for the Eckart barrier using the conventional quantum-mechanical propagation and the quantum trajectory dynamics with the approximate quantum potential. N(E ...


Computation Of Correlation Functions And Wave Function Projections In The Context Of Quantum Trajectory Dynamics, Sophya V. Garashchuk Jan 2007

Computation Of Correlation Functions And Wave Function Projections In The Context Of Quantum Trajectory Dynamics, Sophya V. Garashchuk

Faculty Publications

The de Broglie-Bohm formulation of the Schrödinger equation implies conservation of the wave functionprobability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase ...


Semiclassical Application Of The Mo/Ller Operators In Reactive Scattering, Sophya V. Garashchuk, J. C. Light Jan 2001

Semiclassical Application Of The Mo/Ller Operators In Reactive Scattering, Sophya V. Garashchuk, J. C. Light

Faculty Publications

Mo/ller operators in the formulation of reaction probabilities in terms of wave packet correlation functions allow us to define the wave packets in the interaction region rather than in the asymptotic region of the potential surface. We combine Mo/ller operators with the semiclassical propagator of Herman and Kluk. This does not involve further approximations and can be used with any initial value representation (IVR) semiclassical propagator. Time propagation in asymptotic regions of the potential due to Mo/ller operators reduces the oscillations of the propagator integrand and improves convergence of the results with respect to the number of ...


Cumulative Reaction Probability In Terms Of Reactant-Product Wave Packet Correlation Functions, Sophya V. Garashchuk, D. J. Tannor Jan 1999

Cumulative Reaction Probability In Terms Of Reactant-Product Wave Packet Correlation Functions, Sophya V. Garashchuk, D. J. Tannor

Faculty Publications

We present new expressions for the cumulative reaction probability (N(E)), cast in terms of time-correlation functions of reactant and product wave packets. The derivation begins with a standard trace expression for the cumulative reaction probability, expressed in terms of the reactive scattering matrix elements in an asymptotic internal basis. By combining the property of invariance of the trace with a wave packet correlation function formulation of reactive scattering, we obtain an expression for N(E) in terms of the correlation matrices of incoming and outgoing wave packets which are arbitrary in the internal coordinates. This formulation, like other recent ...


Correlation Function Formulation For The State Selected Total Reaction Probability, Sophya V. Garashchuk, D. J. Tannor Jan 1998

Correlation Function Formulation For The State Selected Total Reaction Probability, Sophya V. Garashchuk, D. J. Tannor

Faculty Publications

A correlation function formulation for the state-selected total reaction probability, Nα(E), is suggested. A wave packet, correlating with a specific set of internal reactant quantum numbers, α, is propagated forward in time until bifurcation is complete at which time the nonreactive portion of the amplitude is discarded. The autocorrelation function of the remaining amplitude is then computed and Fourier transformed to obtain a reactivity spectrum. Dividing by the corresponding spectrum of the original, unfiltered, wave packet normalizes the reactivity spectrum, yielding the total reaction probability from the internal state, α. The procedure requires negligible storage and just one time-energy ...