@article{BOUSSAID2020108412,
title = "Regular propagators of bilinear quantum systems",
journal = "Journal of Functional Analysis",
volume = "278",
number = "6",
pages = "108412",
year = "2020",
issn = "0022-1236",
doi = "https://doi.org/10.1016/j.jfa.2019.108412",
url = "http://www.sciencedirect.com/science/article/pii/S0022123619304069",
author = "Nabile Boussaïd and Marco Caponigro and Thomas Chambrion",
keywords = "Quantum control, Bilinear Schrödinger equation",
abstract = "The present analysis deals with the regularity of solutions of bilinear control systems of the type x′=(A+u(t)B)x where the state x belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators A and B are skew-adjoint and the control u is a real valued function. Such systems arise, for instance, in quantum control with the bilinear Schrödinger equation. For the sake of the regularity analysis, we consider a more general framework where A and B are generators of contraction semigroups. Under some hypotheses on the commutator of the operators A and B, it is possible to extend the definition of solution for controls in the set of Radon measures to obtain precise a priori energy estimates on the solutions, leading to a natural extension of the celebrated noncontrollability result of Ball, Marsden, and Slemrod in 1982."
}