Stephan De Bievre

Dynamical Localization for the Random Dimer Schrödinger Operator

AbstractWe study the one-dimensional random dimer model, with Hamiltonian Hω=Δ+Vω, where for all x∈

Controlling strong scarring for quantized ergodic toral automorphisms

\mathbb{Z}

Orbital Stability: Analysis Meets Geometry

, Vω(2x)=Vω(2x+1) and where the Vω(2x) are i.i.d. Bernoulli random variables taking the values ±V, V>0. We show that, for all values of Vand with probability one in ω, the spectrum of His pure point. If V≤1 and V≠1/

Scarred eigenstates for quantum cat maps of minimal periods

\sqrt 2

Chaotic dynamics of a free particle interacting linearly with a harmonic oscillator

, the Lyapunov exponent vanishes only at the two critical energies given by E=±V. For the particular value V=1/