Random Numbers and Random Matrices

Quantum chaos meets number theory

Overview

This website is intended to supplement an article (AJP000547) 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.

Mathematica notebook (zipped): RandomMatrix.nb