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4:00 pm Wednesday, October 7, 2009 Geometry-Analysis Seminar: Positive Lyapunov Exponent for Ergodic Schroedinger Operatorsby
Helge Krüger (Rice University) in HB 227- The Lyapunov exponent L(E) describes the average exponential growth of solutions of the Schroedinger equation at energy E. It is well known that for random potentials, the Lyapunov exponent is positive at all energies, and that for quasi periodic ones the Lyapunov exponent is positive ones a critical coupling threshold has been passed. I will consider a large class of Schroedinger operators, the ergodic ones. For these, I will describe a multiscale method to prove positive Lyapunov exponent for most energies E assuming some finite scale initial conditions. I will then discuss how this implies positive Lyapunov exponent for the doubling Schroedinger operator at large coupling.
Submitted by damanik@rice.edu |