  We employ the theoretical framework of positive operator valued measures, to
study Markovian open quantum systems. In particular, we discuss how a quantum
system influences its environment. Using the theory of indirect measurements,
we then draw conclusions about the information we could hypothetically obtain
about the system by observing the environment. Although the environment is not
actually observed, we can use these results to describe the change of the
quantum system due to its interaction with the environment. We apply this
technique to two different problems.
  In the first part, we study the coherently driven dynamics of a particle on a
rail of quantum dots. This tunnelling between adjacent quantum dots can be
controlled externally. We employ an adiabatic scheme similar to stimulated
Raman adiabatic passage, to transfer the particle between different quantum
dots. We compare two fundamentally different sources of decoherence.
  In the second part, we study the dynamics of a free quantum particle, which
experiences random collisions with gas particles. Previous studies on this
topic applied scattering theory to momentum eigenstates. We present a
supplementary approach, where we develop a rigorous measurement interpretation
of the collision process to derive a master equation. Finally, we study the
collisional decoherence process in terms of the Wigner function. We restrict
ourselves to one spatial dimension. Nevertheless, we find some interesting new
insight, including that the previously celebrated quantum contribution to
position diffusion is not real, but a consequence of the Markovian
approximation. Further, we discover that the leading decoherence process is due
to phase averaging, rather than induced by the information transfer between the
colliding particles.
