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 Recovery of Missing Samples with Sparse Approximations

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Benjamin G. Salomon
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Sparse Approximations ◽  
Basis Vectors

In most missing samples problems, the signals are assumed to be bandlimited. That is, the signals are assumed to be sparsely approximated by a known subset of the discrete Fourier transform basis vectors. We discuss the recovery of missing samples when the signals can be sparsely approximated by an unknown subset of certain unitary basis vectors. We propose the use of the orthogonal matching pursuit to recover missing samples by sparse approximations.

Frequency‐time decomposition of seismic data using wavelet‐based methods

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1906-1916 ◽  
Author(s):  
Avijit Chakraborty ◽  
David Okaya
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Spectral Decomposition ◽  
Matching Pursuit ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Matching Pursuit Algorithm ◽  
Processing Algorithms ◽  
Short Time

Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency‐time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time‐ frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale‐translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive‐source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet‐based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.

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.

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