Indirect control of the asymptotic states of a quantum dynamical semigroup
In the dynamics of open quantum systems, the interaction
with the external environment usually leads to a contraction of the
set of reachable states for the system as time increases, eventually
shrinking to a single stationary point. In this contribution we
describe to what extent it is possible to modify this asymptotic
state by means of indirect control, that is by using an auxiliary
system coupled to the target system in order to affect its dynamics,
when there is a purely dissipative coupling between the two systems.
We prove that, also in this restrictive case, it is possible to
modify the asymptotic state of the relevant system, give necessary
conditions for that and provide physical examples. Therefore, in
indirect control schemes, the environmental action has not only a
negative impact on the dynamics of a system, it is rather possible
to make use of it for control purposes.