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arXiv:1306.3247 · Computer Physics Communications

Program for quantum wave-packet dynamics with time-dependent potentials

Claude M. Dion, A. Hashemloo, G. Rahali

Published Sep 29, 2013• 35 citations
arXivHTMLPDF
DOI
10.1016/j.cpc.2013.09.012

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Program for quantum wave-packet dynamics with time-dependent potentials (new version announcement)

Claude M. Dion

wavepacket is a program to simulate the dynamics of a wave packet interacting with a time-dependent potential, with the time-dependent Schrödinger equation being solved on a one-, two-, or three-dimensional spatial grid using the split operator method. This new version fixes bugs present in the original program. Program Title: wavepacket CPC Library link to program files: https://doi.org/10.17632/gnxmkygxrw.1 Licensing provisions: GPLv3 Programming language: C (iso C99) Journal reference of previous version: Comput. Phys. Commun. 185 (2014) 407–414. Does the new version supersede the previous version?: Yes Reasons for the new version: Bug fixes. Summary of revisions: This new version fixes bugs in the program wavepacket [1]. In the original version, the function print_wf_bin, used (optionally) to write out the wave function as a binary file, contained a bug that would result in only part of the full wave function being written out when the program was run in parallel. Additionally, negative values of the parameters nt and/or nprint could lead to the program being stuck in an infinite loop. Additional checks have been added to ensure that both these parameters are positive (or zero). Nature of problem: Solves the time-dependent Schrödinger equation for a single particle interacting with a time-dependent potential. Solution method: The wave function is described by its value on a spatial grid and the evolution operator is approximated using the split-operator method [2,3], with the kinetic energy operator calculated using a Fast Fourier Transform. Additional comments including restrictions and unusual features: Simulation can be in one, two, or three dimensions. The fftw [4] implementation of the fast Fourier transform is used, so the corresponding library must be installed. Serial and parallel versions are compiled from the same source files. The parallel version is based on the Message-Passing Interface (mpi) [5]. C.M. Dion, A. Hashemloo, G. Rahali, Comput. Phys. Commun. 185 (2014) 407–414. M.D. Feit, J.A. Fleck, Jr., A. Steiger, Solution of the Schrödinger equation by a spectral method, J. Comput. Phys. 47 (1982) 412–433. M.D. Feit, J.A. Fleck, Jr., Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules, J. Chem. Phys. 78 (1) (1983) 301–308. http://www.fftw.org http://www.mpi-forum.org

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Motion, tunneling, and quantum revivals of wave packets into systems with distributed potential and boundary walls

Andrey L. Sanin, A. A. Smirnovsky, Andrey T. Bagmanov

Quantum wave dynamics in systems with potential wells, bathers and outer impenetrable walls has been studied using solutions of time-dependent Schrodinger equation. Numerical integration of Schrodinger equation, calculation of dynamical variables and its average values, Fourier-spectra were carried out for different initial conditions and different relations between wave packet energy and bather height. In non-symmetric wells the oscillations of wave packets are accompanied by multistep discrete tunneling of probability fluid from well through barrier. In double well potential (symmetric wells) the temporal scales of oscillations and tunneling were investigated in details. Influence of additional time-dependent potential on quantum wave packet dynamics in above listed systems is also discussed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 23, 2006•0 citations
wavepacket is a program to simulate the dynamics of a wave packet interacting with a time-dependent potential, with the time-dependent Schrödinger equation being solved on a one-, two-, or three-dimensional spatial grid using the split operator method. This new version fixes bugs present in the original program. Program Title: wavepacket CPC Library link to program files: https://doi.org/10.17632/gnxmkygxrw.1 Licensing provisions: GPLv3 Programming language: C (iso C99) Journal reference of previous version: Comput. Phys. Commun. 185 (2014) 407–414. Does the new version supersede the previous version?: Yes Reasons for the new version: Bug fixes. Summary of revisions: This new version fixes bugs in the program wavepacket [1]. In the original version, the function print_wf_bin, used (optionally) to write out the wave function as a binary file, contained a bug that would result in only part of the full wave function being written out when the program was run in parallel. Additionally, negative values of the parameters nt and/or nprint could lead to the program being stuck in an infinite loop. Additional checks have been added to ensure that both these parameters are positive (or zero). Nature of problem: Solves the time-dependent Schrödinger equation for a single particle interacting with a time-dependent potential. Solution method: The wave function is described by its value on a spatial grid and the evolution operator is approximated using the split-operator method [2,3], with the kinetic energy operator calculated using a Fast Fourier Transform. Additional comments including restrictions and unusual features: Simulation can be in one, two, or three dimensions. The fftw [4] implementation of the fast Fourier transform is used, so the corresponding library must be installed. Serial and parallel versions are compiled from the same source files. The parallel version is based on the Message-Passing Interface (mpi) [5]. C.M. Dion, A. Hashemloo, G. Rahali, Comput. Phys. Commun. 185 (2014) 407–414. M.D. Feit, J.A. Fleck, Jr., A. Steiger, Solution of the Schrödinger equation by a spectral method, J. Comput. Phys. 47 (1982) 412–433. M.D. Feit, J.A. Fleck, Jr., Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules, J. Chem. Phys. 78 (1) (1983) 301–308. http://www.fftw.org http://www.mpi-forum.org
Quantum wave dynamics in systems with potential wells, bathers and outer impenetrable walls has been studied using solutions of time-dependent Schrodinger equation. Numerical integration of Schrodinger equation, calculation of dynamical variables and its average values, Fourier-spectra were carried out for different initial conditions and different relations between wave packet energy and bather height. In non-symmetric wells the oscillations of wave packets are accompanied by multistep discrete tunneling of probability fluid from well through barrier. In double well potential (symmetric wells) the temporal scales of oscillations and tunneling were investigated in details. Influence of additional time-dependent potential on quantum wave packet dynamics in above listed systems is also discussed.