Quantum dynamical semigroups generated by noncommutative unbounded   elliptic operators
  We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola's sufficient conditions for conservativity to show that the semigroups are conservative. 
C. Bahn, C. K. Ko, Y. M. Park