Alexander C. R. Belton, Stephen J. Wills
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of various strongly continuous quantum dynamical semigroups on C* algebras. The construction is possible provided the generator satisfies an invariance property for some dense subalgebra A_0 of the C* algebra A and obeys the necessary structure relations; the iterates of the generator, when applied to a generating set for A_0, must satisfy a growth condition. Furthermore, either the subalgebra A_0 is generated by isometries and A is universal, or A_0 contains its square roots. These conditions are verified in three cases: the symmetric quantum exclusion processes, as introduced by Rebolledo, and flows on the non-commutative torus and the universal rotation algebra.
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http://arxiv.org/abs/1209.3639
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