Why are dirty metals bad conductors?
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
Time: 3:35pm - 4:25pm