scholarly journals Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics

2017 ◽  
Vol 13 (9) ◽  
pp. 4034-4042 ◽  
Author(s):  
Samuel M. Greene ◽  
Victor S. Batista
Keyword(s):  
Fourier Transform ◽  
Quantum Dynamics ◽  
Split Operator

Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

2005 ◽  
Vol 122 (11) ◽  
pp. 114114 ◽  
Author(s):  
Yinghua Wu ◽  
Michael F. Herman ◽  
Victor S. Batista
Keyword(s):  
Fourier Transform ◽  
Quantum Dynamics ◽  
Matching Pursuit ◽  
Split Operator

Higher order exponential split operator method for solving time-dependent Schrödinger equations

1992 ◽  
Vol 70 (2) ◽  
pp. 555-559 ◽  
Author(s):  
André D. Bandrauk ◽  
Hai Shen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Operator Method ◽  
Computation Time ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exponential Form ◽  
Operator Solution ◽  
Split Operator

A new method of splitting exponential operators is proposed for the exponential form of the operator solution to the time-dependent Schrödinger equation. The method is shown to hold for any desired accuracy in the time increment. A comparison of different algorithms is made as a function of accuracy and computation time. Keywords: splitting operator, Fast Fourier Transform (FFT), Schrödinger equations.

scholarly journals The Phase–Space Approach to time Evolution of Quantum States in Confined Systems: the Spectral Split–Operator Method

2019 ◽  
Vol 29 (3) ◽  
pp. 439-451
Author(s):  
Damian Kołaczek ◽  
Bartłomiej J. Spisak ◽  
Maciej Wołoszyn
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Quantum Dynamics ◽  
Operator Method ◽  
Time Evolution Operator ◽  
Energy Profiles ◽  
Split Operator ◽  
Energy Expectation ◽  
Space Approach ◽  
Confined System

Abstract Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

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