The Peierls barrier in one dimensional models

Dynamical Systems Working Seminar
Friday, February 12, 2016 - 13:00
1 hour (actually 50 minutes)
Skiles 170
Georgia Tech
The Peierls barrier is an observable which  characterizes  whether the the set minimizers with a prescribed frequency  of a periodic variational problem form a continuum or have gaps. In solid state physics Peierls barrier characterizes whether  ground states with a fixed density are  pinned  or are  able to slide. The Peierls barrier is  a  microscopic explanation of static friction. Remarkably, in dynamical systems, Peierls barrier  appears also as  characterizing whether KAM circles break down into Cantor sets.  Hence, the Peierls barrier has been investigated both by physicists and by mathematicians using a variety of methods. We plan to cover the basic definitions of the variational models and some of the basic results obtainedfrom the 80's.