Wednesday, June 12, 2019

One dimensional quasi-periodic Schrödinger operators and quasi-periodic SL(2,R) cocycles

Ao Cai
(CMAFcIO Univ Lisboa)

Abstract: We recall the basic definitions of the two concepts and show the strong relations between them. We establish (almost) reducibility methods to obtain the dynamical properties of q-p SL(2,R) cocycles and then study the spectral theory of 1-d q-p Schrödinger operators. For instance, in the local finitely differentiable case we will show the process of proving the 1/2 Hölder continuity of Lyapunov exponents and the integrated density of states by almost reducibility.

Wednesday, June 12, 2019
Time: 14h00
Room: C6.2.33, Faculdade de Ciências, UL