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Shortcuts to adiabaticity for ultracold gases
In this thesis I explore the possibility of accelerating adiabatic processes for quantum systems. Experiments are performed with a trapped ultracold gas of Rubidium-87... -
Random data for Schrödinger equations : construction of global solutions for ...
In this thesis, we build a large number of global solutions for many supercritical Schrödinger equations. The method is to make the random initial data, using the same... -
Harmonic oscillator with power-law increasing time-dependent e ffective mass
International audience -
Rapid stabilization and observation of oscillating systems at different time ...
This works contains two independent parts, each one dealing with the control of partial differential equations. In the first part, we study an explicit and already... -
Random weighted Sobolev inequalities on $\mathbb{R}^d$ and application to Her...
International audience -
On random Hermite series
We study integrability and continuity properties of random series of Hermite functions. We get optimal results which are analogues to classical results concerning... -
A note on the normalization of the momentum eigenfunctions and Dirac delta fu...
We determine the generating function of the harmonic oscillator by a new method. Using this generating function we derive the eigenfunctions of the moment p. We find... -
Probabilistic global well-posedness for the supercritical nonlinear harmonic ...
Thanks to an approach inspired from Burq-Lebeau \cite{bule}, we prove stochastic versions of Strichartz estimates for Schrödinger with harmonic potential. As a...
