Transition lines for Almost Mathieu Operator

Series: 
Math Physics Seminar
Wednesday, November 7, 2018 - 4:00pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
Organizer: 
I will talk about what happens on the spectral transition lines for the almost Mathieu operator. This talk is based on joint works with Svetlana Jitomirskaya and Qi Zhou. For both transition lines \{\beta(\alpha)=\ln{\lambda}\} and \{\gamma(\alpha,\theta)=\ln{\lambda}\} in the positive Lyapunov exponent regime, we show purely point spectrum/purely singular continuous spectrum for dense subsets of frequencies/phases.