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Prochain séminaire

Mercredi 3 mai

14h00 – 15h00, Amphi 5 du CPT

Formule de Figotin-Pastur pour des opérateurs de Schrödinger à potentiel quasi-périodique et aléatoire

Florian Metzger (Université Aix-Marseille,I2M)


We are interested in the Lyapunov exponent of ergodic Schrödinger cocycles when those have potentials that are mixed quasi-periodic and random.
These cocycles occur in the analysis of solutions to the discrete Schrödinger equation on $\mathbb Z$ at energy E where the potential is defined with that type of ergodic dynamics :
[-(u_n+1+u_n-1)+v_n u_n = E u_n\textrm with v_n=\lambda (W_n(\omega)+V(x+n\alpha)).]
Many results have been obtained separately in the purely quasi-periodic (Dinaburg-Sinai, Bourgain, Goldstein, Avila, Jitomyrskaya, etc.) or purely random cases (Thouless, Aizenmann-Molchanov, Figotin-Pastur, Chulaevsky and Spencer, Sadel and Schulz-Baldes, etc.).
We will expose our main result for the mixed potential : an asymptotic development for the Lyapunov exponent of Schrödinger cocycles at small coupling ($\lambda\to 0$) similar to the pre-existing results in the non-mixed regimes, with some restrictions on the energy parameter $E$.

Séminaires à venir