# Centre de Physique Théorique

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# Séminaires

## Prochain séminaire

### Mercredi 3 mai

14h00 – 15h00, Amphi 5 du CPT

### Résumé

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 $E$.

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Pierre Van Hove (Institut de Physique Théorique, CEA)

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Jeremy Green (DESY)

## TBA

Stephan De Bièvre (Université Lille1, Laboratoire Paul Painlevé)

## TBA

Michele Arzano

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Vojkan Jaksic (Department of Mathematics and Statistics, McGill University, Canada)

## Séminaire d’interêt général

Philip J. Morrison (Department of Physics, University of Texas at Austin)

## TBA

Laurent Baratchart, (Université de Nice Sophia-Antipolis,INRIA)

## Absence of eigenvalues of Schrödinger operators with complex potentials

David Krejcirik (Department of Mathematics, Czech Technical University, Prague, République tchèque)

## On the adiabatic theorem when eigenvalues dive into the continuum

Horia Cornean, (Aalborg University, Danemark)

avril 2017 :