Related papers: Generic controllability properties for the bilinea…
In this paper we prove an approximate controllability result for the bilinear Schr\"odinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schr\"odinger operator than those…
We prove approximate controllability of the bilinear Schr\"odinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and…
In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of…
We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schr\"odinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability,…
We prove that the Schr\"odinger equation is approximately controllable in Sobolev spaces $H^s$, $s>0$ generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining…
We consider a system of an arbitrary number of \textsc{1d} linear Schr\"odinger equations on a bounded interval with bilinear control. We prove global exact controllability in large time of these $N$ equations with a single control. This…
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…
This the text of a proceeding accepted for the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). We present some results of an ongoing research on the controllability problem of an abstract bilinear…
A variety of physically relevant bilinear Schr\"odinger equations are known to be approximately controllable in large times. There are however examples which are approximately controllable in large times, but not in small times. This…
The goal of this work is to prove global controllability and stabilization properties for the fractional Schr\"odinger equation on $d$-dimensional compact Riemannian manifolds without boundary $(M,g)$. To prove our main results we use…
We prove controllability of the Schr\"odinger equation in $\mathbb{R}^d$ in any time $T > 0$ with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schr\"odinger…
We prove global internal controllability in large time for the nonlinear Schr\"odinger equation on some compact manifolds of dimension 3. The result is proved under some geometrical assumptions : geometric control and unique continuation.…
We consider the bilinear Schroedinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to construct controls for the global…
We study the small-time approximate controllability of bilinear Schr{\"o}dinger equations, where the drift is a magnetic Schr{\"o}dinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in…
We prove that the multidimensional Schr\"odinger equation is exactly controllable in infinite time near any point which is a finite linear combination of eigenfunctions of the Schr\"odinger operator. We prove that, generically with respect…
We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric field (the control). We prove the controllability of this system, in any positive time, locally…
We prove global internal controllability in large time for the nonlinear Schrodinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use…
Strichartz estimates, well-posedness theory and long time behavior for (nonlinear) Schr\"odinger equations on waveguide manifolds $\mathbb{R}^m \times \mathbb{T}^n$ are intensively studied in recent decades while the corresponding control…
We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We…
The bilinear control problem of the Schr\"odinger equation $i\frac{\partial}{\partial t}\psi(t)$ $=(A+u(t) B)\psi(t)$, where $u(t)$ is the control function, is investigated through topological irreducibility of the set…