Random numbers and random matrices: quantum chaos meets number theory
A website to accompany an article published in the American Journal of Physics
by Todd Timberlake
[Overview] [Mathematica Code] [ETC]
Overview
This website is intended to supplement an
article that was published in the American
Journal of Physics 74, 547-553 (2006). The article illustrates some statistical properties of random number sequences
and eigenvalues of random Hermitian matrices. The connections between these statistical properties
and those of quantum eigenvalues are illustrated, using the quantum standard map as a model. The article
also discusses some connections between these statistical properties and certain problems in number theory.
The Mathematica Code
Below are links to a Mathematica notebook that can be used to carry out the
calculations discussed in the paper (and more!). Along with the code is a brief description of
what the code actually does. Hopefully this information, combined with the
descriptions in the article, will allow anyone to use these computational
tools on their own. Please feel free to use, modify, and distribute my Mathematica
code as you see fit (although an attribution would be nice).
The Mathematica notebook was created using Mathematica 5.0, but it should also
work in Mathematica 4.0 or later (and possibly even in earlier versions).
You can read the file (without executing it) using the free
MathReader software
from Wolfram Research.
Etc...
If you have any questions or problems with the Mathematica code, please email Todd Timberlake
at ttimberlake@berry.edu
Todd K. Timberlake (ttimberlake@berry.edu)