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. We then apply our results to a quantum mechanical system.
Bibliographical noteFunding Information:
The authors would like to thank their anonymous referees for suggestions to improve the paper. This work was supported by Korea Research Foundation Grant (KRF-2003-005-00010, KRF-2003-005-C00011).
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics