Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).
One of the most active and unusual applications of ensembles is random
matrix theory. It is used to describe phenomena in nuclear physics,
mesoscopic quantum mechanics, and wave phenomena. Random matrix theory
was invented in a bold attempt to describe the statistics of energy level
spectra in nuclei. In many cases, the statistical behavior of systems
exhibiting complex wave phenomena - almost any correlations involving
eigenvalues and eigenvectors - can be quantitatively modeled using simple
ensembles of matrices with completely random, uncorrelated entries!
This is an exercise that not only addresses fundamental issues of universality in spectra, but also is a simple introduction to generating random numbers, eigenvalues, and plotting.
Last modified: August 24, 2006
Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).