Conference - DimaScat : Scattering Theory and Spectral Asymptotics of Differential Operators - in Honour of Dimitri Yafaev

Thursday, April 21, 2016 - 11:30 to 12:30
Didier Robert
Université de Nantes
Irregular time dependent perturbations of quantum Hamiltonians
Abstract: 

Our main goal is to prove existence (and uniqueness) of the quantum propagator for time dependent quantum Hamiltonians $\widehat{H}(t)$ when this Hamiltonian is perturbed with a quadratic white noise $\dot{\beta}\widehat{K}$. $\beta$ is a continuous function in time $t$, $\dot{\beta}$ its time derivative and K is a quadratic Hamiltonian. $\widehat{K}$ is the Weyl quantization of $K$. In our approach we use an exact Hermann Kluk formula to deduce a Strichartz estimate for the propagator of $\widehat{H}(t)+\dot{\beta}\widehat{K}$. This is applied to obtain local and global well posedness for solutions for non linear Schrödinger equations with an irregular time dependent linear part.

Partners

Irmar LMJL ENS Rennes LMBA LAREMA

Affiliation

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL