# Why are dirty metals bad conductors?

## Computational and Applied Mathematics Colloquium

## Meeting Details

For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.

**Speaker:** Dirk Hundertmark, University of Illinois at Urbana-Champaign

**Abstract:** It is a fact of life that dirty metals are bad conductors. But why is this so?
In this talk we will first briefly discuss the model for electrons in a perfect
crystal given by periodic SchrÃ¶dinger operators. In nature there are
no perfect
crystals, however. One will always have randomly distributed
impurities or defects
in the crystalic structure.
In the 1950s, Anderson, a graduate of the UofI high-school (and Nobel prize
winner) invented and studied a model for electrons in a disordered
crystal, now
called the Anderson model. It is the quantum mechanical analogue of a
random walk
in a random environment. Its spectral theory has been extensively
studied both by
Physicists and Mathematicians. I will discuss the mathematical
rigorous results,
with the emphasis on a simple proof of localization (i.e., trapping of
electrons) for large disorder.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 10/31/2008

**Time:** 3:35pm - 4:25pm