Interdisciplinary Stochastic Processes Colloquium

Tuesday November 18;  4.10 - 5.00    room 60 Evans

Speaker: Horng-Tzer Yau (Stanford)

Title: Random Schrodinger Equations

Abstract:
Random Schrodinger equation models electron transport in material with
random impurities. For large disorder, the time evolution of the random
Schrodinger equation is localized (Frohlich-Spencer, Aizenman-Molchanov).
For small disorders, it is conjectured to be diffusive. We shall review a
recent result (jointly with L. Erdos) stating that the random Schrodinger
equation converges to a heat equation under certain scalings. Although
this result does not prove the conjecture, it indicates how the transition
from a time reversible dynamics, i.e., the Schrodinger evolution, to a
time irreversible dynamics may occur.