Details

Autor(en) / Beteiligte

• Beauchard, Karine
• Coron, Jean-Michel
• Rouchon, Pierre

Titel

Controllability Issues for Continuous-Spectrum Systems and Ensemble Controllability of Bloch Equations

Ist Teil von

• Communications in mathematical physics, 2010-06, Vol.296 (2), p.525-557

Ort / Verlag

Berlin/Heidelberg: Springer-Verlag

Erscheinungsjahr

2010

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability is not well understood. We provide several mathematical answers, with discrimination between approximate and exact controllability, and between finite time or infinite time controllability: this system is not exactly controllable in finite time T with bounded controls in L 2 (0, T ), but it is approximately controllable in L ∞ in finite time with unbounded controls in . Moreover, we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin + 1/2 or −1/2.