The analityicity transition in Frenkel-Kontorova models and XY models in 1-D

Math Physics Seminar
Tuesday, October 25, 2011 - 11:05am
1 hour (actually 50 minutes)
Skiles 005
SoM Georgia Tech
 We consider several models from solid state Physics and consider the problem offinding quasi-periodic solutions. We present a KAM theorem that showsthat given an approximate solution with good condition numbers, onecan find a true solution close by. The method of proof leads tovery efficient algorithms. Also it provides a criterion for breakdown.We will present the proof, the algorithms and some conjectures obtainedby computing in some cases.  Much of the work was done with R. Calleja and X. Su.