How Were the Images Produced?
These images were all produced using computers running either Mathematica 4.2 or
Mathematica 5.0.
We used a variety of computers running either Windows 2000 or Windows XP and
with a processor of at least 2.4 GHz and all with 1GB of RAM. We did use
one dual-processor 2.4-GHz machine, but its performance was not substantially
better than the single-processor machines.
Each single-state high-resolution image took about 3 minutes to calculate and
render, while each of the high-resolution Gaussian wave packet images for the
ISW took over 30 hours to calculate and render. The TCL 'splash' images
that are composites of two or three different times, took approximately 4 and 6
days, respectively.
We employed over a dozen computers, each running a different calculation, over
the course of two weeks to produce the high-resolution images in the paper and
the high-resolution images on this Web site.
By high-resolution, we mean two different resolutions. For the
single-state and 2 free-particle Gaussian wave packet images, high-resolution
means 1000 points-per-axis (that is, 106 points in phase space).
For the Gaussian wave packet in the ISW images, high resolution means 400
points-per-axis (that is, 160,000 points in phase space). This 'lower'
resolution is required because of the number of terms in the calculation of this
Wigner function#. The original attempt at 500 points-per-axis
for Gaussian wave packet ISW images resulted in all computers crashing after a
few days.
High-resolution images were necessary to guarantee that the
results reflected the calculation and not an artifact of Mathematica's
interpolation between points. The resulting Mathematica files varied from
12 to 40 MB per file per image rendered.
#Here m
and n are each summed over 40 terms, which yields 160 total terms.
Each of these terms has 4 sub-terms, thereby yielding a total of 640 individual
terms whose sum must be evaluated at 160,000 points in phase space.
© 2004:
M. Belloni, M. A. Doncheski, and R. W. Robinett