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Long time wave packet dynamics from energy eigenfunctions: Nonuniform energy resolution via adaptive bisection fast Fourier transformation
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10.1063/1.2780155
/content/aip/journal/jcp/127/18/10.1063/1.2780155
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/18/10.1063/1.2780155

Figures

Image of FIG. 1.
FIG. 1.

Adiabatic potentials for the two level avoided crossing system of Eq. (12).

Image of FIG. 2.
FIG. 2.

Log plot of the transmitted flux, for a wave packet with and . The solid and dashed lines are for ABFFT (coarse grid of energies plus five stages of bisection, bisection ) and simple FFT (uniform grid of energies), respectively. The results from ABFFT overlap the results from a uniform grid of energies, with difference less than the thickness of the line. The dotted line is wave packet propagation data from Ref. 14.

Image of FIG. 3.
FIG. 3.

Log plot of the reflected flux for a wave packet of and . Results obtained using ABFFT (same grid as in Fig. 2) and wave packet propagation data from Ref. 14—solid and dotted lines, respectively. Again, the difference between these ABFFT results and those for a uniform grid with energies is less than the thickness of the line. In fact, in this case a uniform grid of energies is sufficient to reproduce these results.

Image of FIG. 4.
FIG. 4.

As in Fig. 3, except , both reflected and transmitted fluxes are shown—panels (a) and (b), respectively. Note that the uniform grid of energies does not reproduce the higher resolution data.

Image of FIG. 5.
FIG. 5.

As in Fig. 4, except and the dotted line is for a uniform grid of energies, i.e., there is now discernible but small difference between these data. Note that wave packet propagation data match the uniform grid data almost perfectly in this case.

Image of FIG. 6.
FIG. 6.

Log plot of the long time reflected flux up to , for a wave packet with and , obtained using ABFFT (same grid as in Fig. 2) and a uniform grid of energies—solid and dotted lines, respectively.

Image of FIG. 7.
FIG. 7.

As in Fig. 6, except for transmitted flux, and only the ABFFT results (same grid as in Fig. 2) are shown.

Image of FIG. 8.
FIG. 8.

(solid line) and the base line (dotted line) as a function of energy, evaluated at . 13 resonances with mixed Lorentzian and dispersion profiles are evident (just barely). The inset blows up the first resonance and reveals the associated base line, not visible in larger energy range plot.

Tables

Generic image for table
Table I.

Mean relative error in transmitted flux: (A) from ABFFT, using a uniform coarse grid of 8192 energies (stage 1) and extra points from bisections (i.e., higher stages) using and (B) from simple FFT using the corresponding uniform grid.

Generic image for table
Table II.

Mean relative error in transmitted flux for different coarse grids and higher bisection stages, with resolution up to the resolution of a uniform fine grid of energies. Bisection .

Generic image for table
Table III.

Mean relative error in transmitted flux for different bisection thresholds using a fixed uniform coarse grid of energies plus five stages of bisection.

Generic image for table
Table IV.

Mean relative error in reflected and transmitted flux for wave packets with and 9, for a coarse grid of energies, a bisection threshold of 5% and 5 stages of bisections. Total number of .

Generic image for table
Table V.

The resonant and nonresonant integrated transmitted flux densities for wave packets with , 7, and 9.

Generic image for table
Table VI.

Resonance parameters. (Only the intrinsic parameters are reported. The amplitude depends on the wavepacket.)

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/content/aip/journal/jcp/127/18/10.1063/1.2780155
2007-11-13
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Long time wave packet dynamics from energy eigenfunctions: Nonuniform energy resolution via adaptive bisection fast Fourier transformation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/18/10.1063/1.2780155
10.1063/1.2780155
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