QUANTUM DYNAMICAL SEMIGROUPS GENERATED BY NONCOMMUTATIVE UNBOUNDED ELLIPTIC OPERATORS
CHANGSOO BAHN, Chul Ki Ko, Yong‐Moon Park · Reviews in Mathematical Physics · 2006
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 [1] to show that the semigroups are conservative. We then apply our results to a quantum mechanical system.