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- Nabile Boussaid
- 2008

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only twoâ€¦ (More)

We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. Theâ€¦ (More)

- Nabile Boussaid, Marco Caponigro, Thomas Chambrion
- IEEE Transactions on Automatic Control
- 2013

Weakly coupled systems are a class of infinite dimensional conservative bilinear control systems with discrete spectrum. An important feature of these systems is that they can be precisely approachedâ€¦ (More)

- Nabile Boussaid, Marco Caponigro, Thomas Chambrion
- 2012 American Control Conference (ACC)
- 2012

We provide bounds on the error between dynamics of an infinite dimensional bilinear Schrodinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used onâ€¦ (More)

We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie on the fact thatâ€¦ (More)

- Nabile Boussaid, Marco Caponigro, Thomas Chambrion
- 2012 IEEE 51st IEEE Conference on Decision andâ€¦
- 2012

This note presents an example of bilinear conservative system in an infinite dimensional Hilbert space for which approximate controllability in the Hilbert unit sphere holds for arbitrary smallâ€¦ (More)

- Nabile Boussaid, Marco Caponigro, Thomas Chambrion
- 2012 IEEE 51st IEEE Conference on Decision andâ€¦
- 2012

This paper is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, has to be corrected by aâ€¦ (More)

- Nabile Boussaid, PIERO Dâ€™ANCONA, L. Fanelli
- 2009

We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimatesâ€¦ (More)

- Nabile Boussaid, Marco Caponigro, Thomas Chambrion
- 2012 American Control Conference (ACC)
- 2012

In this paper we study the error in the approximate simultaneous controllability of the bilinear Schrodinger equation. We provide estimates based on a tracking algorithm for general bilinear quantumâ€¦ (More)

- Nabile Boussaid
- SIAM J. Math. Analysis
- 2008

We study the behavior of perturbations of small nonlinear Dirac standing waves. We assume that the linear Dirac operator of reference H = Dm + V has only two double eigenvalues and that degeneraciesâ€¦ (More)