Wigner representation of the rotational dynamics of rigid tops

We propose a methodology to design Wigner representations in phase spaces with nontrivial topology having evolution equations with desired mathematical properties. As an illustration, two representations of molecular rotations are developed to facilitate the analysis of molecular alignment in moderately intense laser fields, reaction dynamics, scattering phenomena, and dissipative processes.

Figure 1

Physical meaning of the parameters entering the definition (33) of the quaternions ${\lambda }_k$.