Classical and Quantum Controllability of a Rotating Asymmetric Molecule

We study both the classical and quantum rotational dynamics of an asymmetric top molecule, controlled through three orthogonal electric fields that interact with its dipole moment. The main difficulties in studying controllability these infinite-dimensional systems are presence severe spectral degeneracies drift Hamiltonian nonsolvability stationary free Schrödinger equation, which lead us to apply a perturbative Lie algebraic approach. In this paper we show that, while equations given by system on $$\mathrm{SO}(3)\times {\mathbb {R}}^3$$ controllable for all values constants configurations, Schödinger equation evolution $$L^2(\mathrm{SO}(3){,{\mathbb {C}}})$$ is approximately almost if only not parallel any principal axes inertia rigid body.