Quantum evolution of power-law mixed states

We study mixed quantum states described by a statistical operator real, with quadratic in the position and momentum operators. These states are parameterized as density matrices exhibiting the maximum q-entropy (q-MaxEnt) form. They can be regarded as the mixed-state counterpart of the power-law tail wave packets recently introduced by Lillio and Mantegna (Phys. Rev. Lett. 84 (2000) 1061; 84 (2000) 4516). We study the time evolution of these q-MaxEnt density matrices. We also investigate the main features of their associated position probability distributions. In particular, we focus attention on the convergence of the concomitant moments.