Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability

The aim of this work is to study the controllability of the bilinear Schr\"odinger equation on compact graphs. In particular, we consider the equation (BSE) $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space $L^2(\mathscr{G},\mathbb{C})$, with $\mathscr{G}$ being a compact graph. The Laplacian $-\Delta$ is equipped with self-adjoint boundary conditions, $B$ is a bounded symmetric operator and $u\in L^2((0,T),\mathbb{R})$ with $T>0$. We provide a new technique leading to the global exact controllability of the (BSE) in $D(|\Delta|^{s/2})$ with $s\geq 3$. Afterwards, we introduce the "energetic controllability", a weaker notion of controllability useful when the global exact controllability fails. In conclusion, we develop some applications of the main results involving for instance star graphs

Small-time controllability for the nonlinear Schr\"odinger equation on RN\mathbb{R}^N via bilinear electromagnetic fields

We address the small-time controllability problem for a nonlinear Schr\"odinger equation (NLS) on $\mathbb{R}^N$ in the presence of magnetic and electric external fields. We choose a particular framework where the equation becomes $i\partial_t \psi = [-\Delta+u_0(t)h_{\vec{0}}+\langle u(t), P\rangle +\kappa|\psi|^{2p}]\psi$. Here, the control operators are defined by the zeroth Hermite function $h_{\vec{0}}(x)$ and the momentum operator $P=i\nabla$. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals $u_0$ and $u$. We first show the existence of a family of quantum states for which this property is verified. Secondly, by considering some specific states belonging to this family, as a physical consequence we show the capability of controlling arbitrary changes of energy in bounded regions of the quantum system, in time zero. Our results are proved by exploiting the idea that the nonlinear term in (NLS) is only a perturbation of the linear problem when the time is as small as desired. The core of the proof, then, is the controllability of the bilinear equation which is tackled by using specific non-commutativity properties of infinite-dimensional propagators.Comment: 15 page

Finite-top-mass effects in NNLO Higgs production

We construct an accurate approximation to the exact NNLO cross section for Higgs production in gluon-gluon fusion by matching the dominant finite top mass corrections recently computed by us to the known result in the infinite mass limit. The ensuing corrections to the partonic cross section are very large when the center of mass energy of the partonic collision is much larger than the Higgs mass, but lead to a moderate correction at the percent level to the total Higgs production cross section at the LHC. Our computation thus reduces the uncertainty related to these corrections at the LHC from the percent to the per mille level.Comment: 4 pages, 4 figures; to be published in the proceedings of QCD2008. Reference adde

Support to Design for Air Traffic Management: An Approach with Agent-Based Modelling and Evolutionary Search

This paper presents a methodology to manage the support to design in ATM operations. We propose a workflow for the design of ATM solutions in a performance-based setting. The methodology includes the evaluation of the impact on human behaviour and exploits a combination of different paradigms, such as Agent-Based Modelling and Simulation, and Agent-Based Evolutionary Search. We prove the soundness of the methodology by carrying out a real case study, which is the transition from Direct Routing to Free Routing in the Italian airspace. The validation results exhibit limited errors for the assessment of the performance metrics under evaluation. Furthermore, the optimization of sector collapsing/decollapsing configuration is discussed to demonstrate the effectiveness of the implemented engines